The SIMPLEST Way to Answer Speed, Distance and Time Questions GCSE MATHS

hey guys welcome back to another gcsc math video this time we're going to be looking at speed distance time but I'm going to show you a method that I've started teaching which is in my opinion a lot easier to understand uh it's less likely to lead to mistakes and it makes the actual math easier if it's a non- calculated paper and so I want to give you a bit of an introduction but before we start most of the people that watch these videos are unsubscribed so if you could consider just quickly pressing that subscribe button that would really help me out and I'd really appreciate it um my link to my website and my email address are in the description in case you have any questions or like some tutoring but let's get straight into it to introduce this method to you I'm going to write out 40 mph and if any of you have been in a car you've probably seen a speed like this many times before right 30 m hour 40 m hour 60 M hour Etc but what does this actually mean what this means is that in 1 hour we travel 40 m right logically 40 m per hour don't forget that P stands for per per means for every hour we travel we travel 40 mil that means in 2 hours we should travel 80 mil in 3 hours we should travel 120 miles so as you can see we have this kind of direct proportion set up where as we increase the number on the left the right increases by the same amount so for example going from 1 to two is the same as timesing by two so we time both sides by two nice and easy so we have this direct proportion so this method also works for direct proportion and even inverse proportion which is really really nice but again we'll get to that maybe in another video and so we can use this to you know work out pretty much any value we want and we can even go down to maybe half an hour half an hour will be 30 minutes and again we divide both sides by two so to me this makes it really really logical and it's really easy to see what we're looking for so let's actually try and apply it to a question so it says here a car travels 90 m in 3 hours and we need to work out the speed so I'm going to literally just write the information they've given me we've traveled 90 miles in 3 hours now if we think about the unit we use for Speed if I go back for a second it's miles per hour and remember per means for every 1 hour how far do we travel so in other words I'm trying to get down to 1 hour and all you do is you ask yourself how did you go from 3 to 1 ideally by timesing or dividing well all I do is I divide by three so what should I do to the other side I divide by three that means for each hour we travel 30 m so in other words we are traveling at 30 m hour and that's it you don't have to worry about the formula triangle the reason why I dislike the formula triangle personally is because a lot of students forget which way around it goes which is understandable so imagine you're in an exam you're under pressure your memory is going to be worse than what it usually is so memorize this is a bit of a waste of time now for those of you that know how to do the formula brilliant if you know the formula you can rearrange the formula Etc but I think you'll agree that this is quite nice and elegant and it's quite simple so again 200 mil in 4 hours now another question that students ask me is well what does it mean by average speed do I have to like take a mean or something and that's a very fair question what they're essentially saying when we work out the speed in this case you know when you're driving a car or a train they do not stay at the same speed forever right they don't just travel at you know 30 mph instead it goes up and goes down we're just talking about the average speed because we're not taking into account any changes in the speed so when we do this method we get the average speed anyway so again I ask myself how do I get to 1 hour because again we want miles per hour so we want just a a 1 hour increment we divide by four so divide both sides by four and what do we get we get 50 miles in 1 hour so that means we are traveling at 50 miles per hour which is really really nice now here's where gets a bit trickier is when they give it to you in minutes what can you do well again I'm going to write the exact same thing 60 miles in 90 minutes and there are are a few different things that you can do to help yourself out here some people like to try and get down to 60 minutes so if I write that and sorry that's just say minutes not miles and I'll think to yourself why do we want to get to 60 minutes we want to get to 60 minutes because there are 60 Minutes in 1 hour simply put now this is kind of hard to spot what can I divide 90 by to get to 60 well there is a number you can divide but it's hard to spot so instead what could I do well I could go down to half an hour 30 minutes and then go up to 60 minutes right there's no harm in doing that that's completely fine that's legal so if I divide both sides by three I get 20 mil in 30 minutes and then I'm going to times both sides by two and I get 40 mil in 60 minutes in other words I get 40 mil in an hour in other words I have 40 mil per hour now what was the other way I mentioned well I could call this 1.5 hours 1 and a half hour right and then divide by 1.5 now some people don't like dividing by 1.5 cuz a bit scary uh let me show you how you do that quickly so you have 60 / 1.5 you want to get rid of the decimal so it times both sides by 10 so we have 600 ID 15 and then you just use the classic bus stop method or you could think to yourself how many 15s going to 60 that's four add on the Zero you should get 40 but let's let me prove it to you so 15 into 6 is 0 remainder six that' be four and then add the zero you still get 40 mil an hour so it's the same thing you don't really have to worry too much about that but I just wanted to show you just to be sure I covered all the bases again 30 mil in 30 minutes average speed well we have 30 miles in 30 minutes and again we want to get up to an hour because we want miles per hour because that's what we normally use as our unit of speed so I'm going to Times by two we get 1 hour or 60 Minutes depending on how you want to write it it's a free country you can do what you want and we get 60 miles in 60 minutes in other words we get 60 miles hour so let's move on to actually calculating things like distance and time so here's a good question how do we get backwards to travel can we still use this method the answer is absolutely first we write down the information they've given us it says 40 mil hour so in other words we have 40 miles in 1 hour right that's still the same thing as usual but now it's asking me Jim travels at 40 m an hour for 3 hours how far did he travel well I'm going to write 3 hours underneath and what we're trying to do is work out the distance he travels in 3 hours well if he travels 40 mil in 1 hour he should travel 120 miles in 3 hours because again we've gone from 1 hour to 3 hours if he's traveling at 40 m every hour that means he's going 40 second hour 80 third hour 120 in other words we times both sides by three and that's it so here again for 15 minutes Sally ran out an average speed of 20 km an hour so again let's write that down we have 20 km in 1 hour now it says about 15 minutes so you could write that as a quarter of an hour but if you are unsure here's what you could do you could change the units to minutes and then you ask yourself what do you divide 60 by to get 15 you divide it by four that's why it's a quarter of an hour so that means 20 ID 4 true travels 15 km sorry 5 K in 15 minutes nice and easy and here's the last thing you can be asked so we've done calculating speed we've done calculating uh dist yeah distance now the last thing is to calculate time and people say again do I have to use the formula no because again let's write this out 60 M hour so we have 60 mil in 1 hour and what does it say it says a train travels at 300 M at 60 MPH how long did this take well let's put 300 miles under here all we're doing again is working out how many times bigger 300 is than 60 and timesing it by this so all we need to do is do 300 / 60 we can cross out a zero that's 30 / 6 which is five so we've times 60 by 5 to get 300 miles so we just need to times the time by five to get 5 hours and so how long did it take it took 5 hours and again in the previous questions what distance did she run you could just highlight that as your answer just to be sure but yeah this works for Speed distance and time and even for direct and indirect proportion sorry inverse proportion here's a good one to kind of finish up on so Runner travels 3 km at 5 m/ Second how long did they take well again we have 5 m in 1 second but we're trying to find three kilom now the problem here is is the units are different so how many meters are in are in 3 km when you just Times by 1,00 so now is a good question what do we times 5 by to get to 3,000 well the best way to do this is to do 3,000 / 5 so that's 0 60 0 so we times it by 600 so mean we times the time by 600 so it takes us 600 seconds or uh 10 minutes in order to run 3,000 M now hopefully I've Illustrated how useful this method is again we've used some exam style questions but of course the problem solving questions can get a bit trickier so let me know if you'd like me to go through those in the comments but again this method is really really useful because the best piece of advice I ever got given is to keep things simple the simpler you keep it the less likely you are to make mistakes so if you can use the formula triangle okay but what if you make mistakes with that have you ever made a mistake with the formula triangle have you ever made a mistake with rearranging the answer is probably yes this it's a lot harder to make a mistake because it's basic it's simple you can even use this with a calculator right because you know all we're doing is work what we're timesing by you can work that out even easier using a calculator