A car is travelling at a speed of 25 meters per second. What is the speed of the car in kilometers per hour?
Okay, so in this question, we’ve been given some information about a car. We’ve been told that it’s moving at 25 meters per second. Now, we’ve been asked to take this speed 25 meters per second and express it in different units, specifically kilometers per hour. In other words, what is the value in kilometers per hour of the same speed, 25 meters per second? And so, this is the conversion we’re being asked to find, 25 meters per second to, let’s say, 𝑥 kilometers per hour. And we’re trying to find the specific value of 𝑥.
To do this, we’ll have to recall the conversion between meters and kilometers and seconds and hours. So we can start by recalling that one kilometer is equivalent to 1000 meters. That’s what the prefix “kilo” means. It means 1000. And we can also recall that one hour is equivalent to 60 multiplied by 60 seconds because every hour has 60 minutes in it and every minute has 60 seconds in it. Therefore, every hour has 60 times 60 seconds in it.
Now, in this particular question, we’re converting from meters to kilometers and from seconds to hours. Therefore, we need to take both of these relationships that we’ve just recalled and rearrange them so that we’ve got firstly kilometers in terms of one meter. So that instead of the unit meters here, we can replace it with the equivalent number of kilometers. And similarly, we want the equivalent number of hours to one second so that we can take the unit second here and replace it with the equivalent number of hours.
So let’s start by rearranging this first expression here. One kilometer is equal to 1000 meters. Well, we can do this by dividing both sides of the equation by 1000. We find then that one divided by 1000 kilometers or one 1000th of a kilometer is equal to one meter. And if we realize that 60 multiplied by 60 is 3600, we can do a similar sort of thing for the equation, linking hours to seconds. We can divide both sides of the equation by 3600. When we do this, we find that one divided by 3600 hours is equal to one second. And at this point, what we can do is to say that one meter per second is equal to one 1000th of a kilometer divided by one 3600th of an hour. Because this numerator is equivalent to one meter and this denominator is equivalent to one second.
And notice the units we have on the right-hand side of this equation. We’ve got kilometers in the numerator and hours in the denominator. So the unit overall is kilometers per hour. All we need to do is to deal with the numerical value. And so, we can separate off the unit kilometers per hour and just deal with the numerical value by itself, which ends up being one over 1000 divided by one over 3600.
Now, in this case, we’ve got a fraction divided by a fraction. And we can recall that a general mathematical rule is that when we have a fraction divided by a fraction, we can, firstly, write this in a slightly different way as 𝑎 over 𝑏 — that’s the numerator of this fraction — divided by 𝑐 over 𝑑 — that’s the denominator of this fraction. And then, we can recall that this expression on the right-hand side is mathematically equivalent to multiplying the first fraction by the reciprocal or inverse of the second fraction. In other words, we can think of this as changing the division sign to a multiplication sign and flipping the second fraction, so 𝑑 over 𝑐 rather than 𝑐 over 𝑑, which looks like this when tidied up a bit.
Now, we can apply this mathematical rule to the numerical value that we have on the right-hand side of our equation here. In this case, our value of 𝑎 is one, 𝑏 is 1000, 𝑐 is one, and 𝑑 is 3600. And therefore, our numerical value becomes one over 1000 multiplied by 3600 over one. Then, we simply multiply the numerators together and the denominators together separately, leaving us with one times 3600 divided by 1000 times one. Now, one times 3600 in the numerator is simply 3600 and 1000 times one in the denominator is simply 1000. At this point, we can simplify the fraction by dividing 3600 by 1000, which leaves us with a numerical value of 3.6.
In other words then, one meter per second is equivalent to 3.6 kilometers per hour. And therefore, the speed that we were trying to convert from meters per second to kilometers per hour can now be converted because we can take the conversion factor that we’ve just found and multiply both sides of that equation by 25. This gives us 25 meters per second on the left-hand side. And on the right-hand side, we have 25 times 3.6 kilometers per hour. The numerical value 25 times 3.6 ends up being 90.
And hence, at this point, we found our answer to the question. 25 meters per second is equivalent to 90 kilometers per hour.