WEBVTT
00:00:02.730 --> 00:00:07.500
Two cars traveled from city A to city B along a route which is 54 kilometers long.
00:00:08.150 --> 00:00:10.260
They both departed city A at the same time.
00:00:10.830 --> 00:00:19.640
If the speed of the first car was 40 kilometers per hour and the speed of the second car was 60 kilometers per hour, what is the time difference between their arrival times at city B?
00:00:20.370 --> 00:00:21.860
Give your answer in minutes.
00:00:23.390 --> 00:00:30.170
So in this question, what we’re gonna look at is how much time it took for car one and then car two to complete the journey from city A to city B.
00:00:30.170 --> 00:00:32.780
And then we’re gonna compare these times.
00:00:34.490 --> 00:00:39.460
So to enable us to work out what we want to, then what we’re gonna use is a speed–distance–time triangle.
00:00:39.880 --> 00:00:45.550
And what this does is helps us work out the formula for which one of the elements we want to find, either speed, distance, or time.
00:00:47.490 --> 00:00:50.090
Well, in this question, what we’re trying to find out is the time taken.
00:00:50.850 --> 00:00:57.170
So we can see from this triangle that time is equal to the distance divided by the speed.
00:00:57.540 --> 00:00:58.100
Okay, great!
00:00:58.440 --> 00:01:00.830
So now, let’s see what information we’ve been given in the question.
00:01:02.660 --> 00:01:07.960
Well, we can see that the distance with both of the cars, so car one and car two, is gonna be 54 kilometers.
00:01:08.480 --> 00:01:11.080
And that’s because both of the cars took the same route.
00:01:12.880 --> 00:01:20.480
And then we can see that the speed of the first car is 40 kilometers per hour and the speed of the second car is 60 kilometers per hour.
00:01:22.050 --> 00:01:26.680
Then what we do before we carry out any calculations is check that the same units are used throughout.
00:01:26.680 --> 00:01:31.830
And we can see here that it’s kilometers cause we’ve got kilometers and kilometers per hour, so this means this is gonna work.
00:01:31.830 --> 00:01:38.750
And we do that because if it was different units — for instance, miles or meters or something like that — then the calculations would not be correct.
00:01:38.750 --> 00:01:41.610
So we’re gonna start with car one.
00:01:41.930 --> 00:01:47.600
And to carry out the calculation here, we’re gonna do time is equal to 54 divided by 40 cause it’s distance divided by speed.
00:01:49.090 --> 00:01:50.930
Well, what we can do here is work in fractions.
00:01:51.600 --> 00:01:56.940
And we can see that it turns into a mixed number because 40 goes into 54 once remainder 14.
00:01:57.240 --> 00:02:04.750
So we’ve got one and fourteen fortieths, which we can then simplify further by dividing the numerator and denominator by two.
00:02:05.230 --> 00:02:07.690
So we get one and seven twentieths of an hour.
00:02:08.090 --> 00:02:08.720
Okay, great!
00:02:09.320 --> 00:02:10.470
But what do we want to do now?
00:02:11.960 --> 00:02:16.060
Well, because we’re looking to give the final answer in minutes, what we want to do now is convert this into minutes.
00:02:17.450 --> 00:02:19.300
And when we do this, we get 81 minutes.
00:02:19.440 --> 00:02:25.970
And we get this because there are 60 minutes in an hour, and then seven twentieths is going to be 21 minutes.
00:02:25.970 --> 00:02:27.850
And we add them together, it gives us 81 minutes.
00:02:28.370 --> 00:02:33.050
And seven twentieths, we can work this out in minutes because what we have is seven twentieths of an hour.
00:02:33.410 --> 00:02:37.580
So it’s seven twentieths multiplied by 60 cause that’s the number of minutes in an hour.
00:02:38.140 --> 00:02:42.440
What we can do is divide 60 and 20 through by 20.
00:02:43.050 --> 00:02:44.620
So that’s gonna leave us three and one.
00:02:44.650 --> 00:02:47.470
So then we’ve got seven multiplied by three, which is 21.
00:02:48.090 --> 00:02:48.700
Okay, great!
00:02:48.930 --> 00:02:50.240
So now, let’s have a look at car two.
00:02:51.910 --> 00:02:57.100
Well, for car two, if we wanna find the time, it’s equal to the distance over the speed, so 54 over 60.
00:02:58.890 --> 00:03:02.150
Well, we can think of this as fifty-four sixtieths of an hour.
00:03:02.690 --> 00:03:06.910
Well, because we know there are 60 minutes in an hour, we know this is gonna be 54 minutes.
00:03:09.010 --> 00:03:14.090
Well, we can see that from the question, what we’re trying to find is the difference between the arrival times at city B.
00:03:14.510 --> 00:03:17.740
So what we want to do is compare the amount of time taken by each of the cars.
00:03:19.440 --> 00:03:22.500
So the difference is gonna be equal to 81 minus 54.
00:03:23.970 --> 00:03:29.190
So therefore, we can say that car two will arrive at city B 27 minutes before car one.