in this video we're going to look at speed distance and time we're going to look at some problems involving these so here we've got a car traveling through a speed limit of 30 miles per hour so if the car's traveling at 30 miles per hour its speed will be 30 mph or 30 miles per hour and that means in every hour it drives 30 miles so in one hour it would drive 30 miles 2 hours 60 miles 3 hours 90 miles 4 hours 120 miles or so on and that's what a speed is speed is a measurement of how far you travel in a certain amount of time so quite often in exam questions we'll be looking at miles per hour so how many miles maybe a car or lloyd travels in an hour we could also maybe be looking at kilometers per hour now with kilometers per hour you'd write km h and that would be how many kilometers you travel in an hour so instead of writing p you write the forward slash and or maybe even um it could be meters per second so maybe something like a sprinter or something like that you maybe look at how many meters they travel in a second but all of these speed measure how far you travel in a certain amount of time whether it's an hour an hour or second or so on okay let's look at the speed in a little bit more detail so we have the speed of 30 miles per hour that's where the car is traveling at and in one hour as we said 30 miles per hour it would drive 30 miles in two hours it'll be 60 miles 3 hours 90 miles 4 hours 120 miles 10 hours even 300 miles because 10 lots of 30. so what we'll want to do is just establish a relationship between these okay so if we know that the speed is that the car's traveling at is 30 miles per hour watch this 30 divided by 1 is 30. 60 divided by 2 is 30. 90 divided by 3 is 30. 120 divided by 4 is 30. 300 divided by 10 is 30. so in all these situations whenever you divide the distance that it travels by the time you will always get the speed as long as the time is in you know the unit that you want the speed in okay so here we've got the first one speed is equal to distance divided by time so if we want to find the speed that something is traveling so if we didn't know how far that how fast the car was traveling but i knew perhaps it drove 60 miles in two hours i could do the distance divided by the time and it will give me the speed next um distance is equal to speed times time notice that if the speed is 30 miles per hour and i drove for 10 hours where it's 30 miles in every hour so you do 10 lots of 30 or another quick way of doing that is 10 times 30 and that would be 300. so if we want to find how far something travels if we multiply its average speed its speed by the time that it travels for we will find the distance covered and finally if you want to find the time taken watch this if i travel 300 miles at 30 miles per hour well if i divide 300 by 30 i get 10. so these are three very important formula now i quite often will focus on the words miles per hour and figure out from there but these formulas are a formula are very important to learn sometimes you might see a triangle like this maybe given to you in physics or even mavs where you've got s d and t and what you do is you cover up what you're looking for so if i wanted to find speed i would cover up the s that leaves me with d over t distance divided by time if i wanted to find the distance traveled well if i want to find the distance i cover up the distance and because these are the same level you just do speed times time and if you want to find how long a journey takes if you divide if you cover up the time so put your thumb over time that'll leave you d over s so you do distance divided by speed and that will give you the time taken so this is a quick uh way of remembering it or alternatively you could just figure it out by thinking what miles per hour or you know kilometers per hour remains and you can remember it that way okay and so what we're going to do now is we're going to look at some exam questions so here we've got first one we've got a car traveled uh 180 miles in four hours find the average speed in miles per hour off the car so as we've seen speed is equal to distance divided by time okay or s equals d over t depending on how you want to ride it so the speed is equal to the distance where the distance traveled a car drives 180 miles so 180 miles divided by the time taken well the time taken is four hours so divided by four so we will do 180 divided by four 180 divided by 4 is equal to 45 so that means the car must be traveling at 45 miles per hour and remember to include your units let's just check that so the car travels for four hours well at 45 miles per hour that'd be four lots of 45 so i'd be 45 90 135 180 so yeah in four hours it would cover 180 miles okay next that's not always as we've seen earlier it's not always um miles per hour it might be meters per second and so on kevin runs 400 meters in 50 seconds work out his average speed so again speed is equal to if you cover up s distance divided by t so d over t so speed is equal to the distance 400 meters divided by the time 50 seconds and 400 divided by 50 is equal to eight and this time it's meters per second so m slash s that's it so that's the next question okay a train travels at 170 a train travels 175 miles at an average speed of 25 miles per hour work out how long the journey lasts so how long the journey lasts it wants to know the time that the journey takes so we want to find t in this situation so we want to find h we're going to do t equals distance divided by speed distance divided by speed so time equals well the distance to the train travels in total is 175 miles and the speed at which it travels is 25 miles per hour so if we divide those we're going to find 12 175 divided by 25 well that would be equal to 7 hours that's it so we found out how long the the journey would last next a bird flies for six hours an average speed of 40 kilometers per hour calculate how far the bird travels or how far how far the bird flies so this time we want to find how far it flies that's the distance we want to find the distance so that's going to be speed times time so distance is equal to speed times time so distance is equal to the speed 40 kilometers per hour times the time six hours and 40 times six is equal to 240. now let's just make sure we're getting the right units the speed is 40 kilometers per hour so it's going to be 240 kilometers okay our next example a helicopter flies 200 miles in two hours and 30 minutes calculate the average speed in miles per hour of the helicopter now this question is a bit different than the ones we've looked at so far because if you notice the time has got two different units it's two hours 30 minutes so what we need to do is because we want it miles per hour well again we want to find the speed so the speed is equal to distance divided by time speed is equal to where the distance is 200 but the issue here is the time now we want miles per hour so this needs to be hours on the bottom line now 2 hours 30 minutes for 30 minutes 30 minutes is equal to half an hour so two hours 30 minutes would be equal to two and a half hours so it'll be 2.5 because 30 minutes is half an hour it's quite important to remember that so for instance if you have minutes and you've got hours 30 minutes it's half an hour no 0.5 15 minutes a quarter of an hour that'd be 0.25 45 minutes so that's three quarters of an hour and that'll be 0.75 and so on so it's important to know um you know um what your minutes are in hours alternatively you could just write as a fraction and cancel it down so 30 minutes well that's 30 out of an hour 60 and counting that down as a half anyway so 2 hours 30 minutes with because it's 2 hours 30 minutes is 2.5 so we're going to do distance 200 divided by the time two and a half 2.5 that will give us our speed so 200 divided by 2.5 is equal to 80. so the average speed of the helicopter is 80 miles per hour miles per hour okay next roger drives for 2 hours 15 minutes at an average speed of 30 miles per hour how far does roger drive so we want high five travels so that's going to be distance that's going to be speed times time so distance is equal to speed times time so the distance will be equal to speed 36 miles per hour 36 times the time now again because it's miles per hour we need the time to be in hours now we've got two hours 15 minutes so it's going to be two hours point now 15 minutes is a quarter of an hour so that's going to be 0.25 because 15 minutes is 0.25 hours and because it's two and a quarter hours it's going to be 2.25 hours so we times our 36 by 2.25 and so distance would be equal to 36 times by 2.25 equals 81 miles okay our second last example a car travels at 20 uh sorry a car travels 240 kilometers in three hours 40 minutes calculate the average speed of the car so the speed is equal to distance divided by time so speed is equal to distance divided by time so the speed will be equal to the distance 240 divided by the time now again we've got to be careful here because we want the speed in kilometers per hour so the time will need to be in hours and we've got three hours 40 minutes now i automatically know this is going to be 3.66606 recurring because uh 40 minutes is two-thirds of an hour but let's have a look and see what we do if we don't know that so three hours will be three point now we need to change to 40 minutes into an hour into a decimal of an hour so what i'm going to do is i'm going to write this 40 minutes as a fraction of an hour so 40 minutes out of 60 minutes because that's what you know 40 minutes out of an hour cancel it down that's going to be 4 over 6 and then she can't say that down two-thirds so it's two-thirds so that means that 40 minutes is two-thirds of an hour and two-thirds of an hour and two-thirds is not 0.6 recurring or 0.6666 so on okay or 240 divided by 3.6 with the dot above it okay so 20 minutes is a third of an hour 40 minutes is two thirds of an hour and so on okay so we're going to do the sp the distance 240 divided by 3.6 recurring when we do that 240 divided by 3.6 recurring we get that's equal to 65.8 kilometers per hour and that's to two decimal places and let's just check it if we times the speed by the time we should get the distance so if we times our answer by 3.666 and so on we get that's equal to 240. that's it so the color travels at an average speed of 65.45 kilometers to two decimal places and our last example a lorry travels 210 miles at an average speed of 50 miles per hour calculate how long the journey lasts so we want time that's going to be distance divided by speed so time is equal to distance divided by speed and it says calculate how long the journey lasts give your answer in hours and minutes so time is equal to distance 210 divided by um speed so time is equal to distance divided by speed so 210 divided by the speed 50. so we do 210 divided by 50 and we get that's equal to 4.2 now that's because it's miles per hour that's going to be 4.2 hours now unfortunately we wanted we have not unfortunately but we have to give our answer in hours and minutes so we know it's going to be four hours what we need to do is we need to get our minutes uh from the null point two hours so what we do is we just multiply no point two not 0.2 by 60 minutes because we didn't want to know what 0.2 is of 60. so 0.2 times 60 will be equal to 12. so that means that 0.2 of an hour 0.2 hours is equal to 12 minutes and that means that our journey will last for 4 hours 12 minutes that's it so the important thing to learn from this video is first of all that the relationships between speed distance and time which are speed is distance divided by time distance is speed times time and the time is equal to distance divided by speed and that these can be summarized in a triangle like so with speed distance and time or you can figure it out by just remembering what the units mean miles per hour and you know being aware of that and that's it and just being very careful that if you are dealing with uh questions where you've got hours and minutes to change them into hours or minutes depending on what it you know it needs to be most often you will change them into hours and that if you're looking for a journey in hours and minutes the duration of it what you would do is times the decimal number by the by 60 to find how many minutes that would be well that's it