Two cars traveled from city A to city B along a route which is 54 kilometers long. They both departed city A at the same time. 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? Give your answer in minutes.
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. And then we’re gonna compare these times. So to enable us to work out what we want to, then what we’re gonna use is a speed–distance–time triangle. 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.
Well, in this question, what we’re trying to find out is the time taken. So we can see from this triangle that time is equal to the distance divided by the speed. Okay, great! So now, let’s see what information we’ve been given in the question. Well, we can see that the distance with both of the cars, so car one and car two, is gonna be 54 kilometers. And that’s because both of the cars took the same route. 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.
Then what we do before we carry out any calculations is check that the same units are used throughout. 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. 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.
So we’re gonna start with car one. 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. Well, what we can do here is work in fractions. And we can see that it turns into a mixed number because 40 goes into 54 once remainder 14. So we’ve got one and fourteen fortieths, which we can then simplify further by dividing the numerator and denominator by two. So we get one and seven twentieths of an hour.
Okay, great! But what do we want to do now? Well, because we’re looking to give the final answer in minutes, what we want to do now is convert this into minutes. And when we do this, we get 81 minutes. And we get this because there are 60 minutes in an hour, and then seven twentieths is going to be 21 minutes. And we add them together, it gives us 81 minutes.
And seven twentieths, we can work this out in minutes because what we have is seven twentieths of an hour. So it’s seven twentieths multiplied by 60 cause that’s the number of minutes in an hour. What we can do is divide 60 and 20 through by 20. So that’s gonna leave us three and one. So then we’ve got seven multiplied by three, which is 21. Okay, great!
So now, let’s have a look at car two. Well, for car two, if we wanna find the time, it’s equal to the distance over the speed, so 54 over 60. Well, we can think of this as fifty-four sixtieths of an hour. Well, because we know there are 60 minutes in an hour, we know this is gonna be 54 minutes. Well, we can see that from the question, what we’re trying to find is the difference between the arrival times at city B. So what we want to do is compare the amount of time taken by each of the cars. So the difference is gonna be equal to 81 minus 54. So therefore, we can say that car two will arrive at city B 27 minutes before car one.