Video Transcript
A snail travels at a speed of 0.0025 meters per second. What is its speed in meters per hour?
Okay, so in this question, we are told the speed of a snail in units of meters per second. And we are asked to work out what value the speed has in units of meters per hour. We have our snail. And we know that it’s moving at a speed of 0.0025 meters per second. Now that’s quite a small number, which means quite a slow speed, as we might expect from a snail.
If we want to know the snail’s speed measured in units of meters per hour, then we need to know the conversion between seconds and hours. Now there are 60 seconds in a minute, and there are 60 minutes in an hour. So the conversion between seconds and hours is as follows. We can write that one hour is equal to one hour multiplied by 60 minutes per hour multiplied by 60 seconds per minute. If we look at the units on the right-hand side, we see that the hours will cancel with the per hour and the minutes will cancel with the per minute. So we’re going to get left with a time measured in units of seconds.
And if we do the multiplication, we have 60 multiplied by 60, which gives us a value of 3600. So we have that one hour is equal to 3600 seconds. We can divide both sides of this relation by 3600. On the right-hand side, the 3600s in the numerator and denominator cancel each other out. Then swapping left- and right-hand sides of the equation over, we have that one second is equal to one over 3600 of an hour.
In the question, we had a speed measured in units of meters per second. This is the number of meters traveled per one second of time. But we know that one second is equal to one over 3600 of an hour. So if we take our speed of 0.0025 meters per second, we can replace the per second with per one over 3600 of an hour. And so we have that the speed is equal to 0.0025 meters per one over 3600 of an hour. Tidying this up a little, we can write the speed in units of meters per hour as 0.0025 divided by one over 3600 meters per hour.
All we need to do now is evaluate this numerical value. Notice that we have a number divided by a fraction. Now when we have a number divided by a fraction like this, that is the same as multiplying by the reciprocal of the fraction in the denominator. In fact, we have a general mathematical rule that says if we have a number, 𝑎, divided by a fraction, 𝑏 over 𝑐, then this is equal to that same number 𝑎 multiplied by the fraction 𝑐 over 𝑏, which is the reciprocal of 𝑏 over 𝑐.
If we compare this general rule to our specific case here, we can identify that 0.0025 is equal to 𝑎, our one here is equal to 𝑏, and the 3600 is equal to 𝑐. So we can rewrite our speed. Rather than dividing by the fraction one over 3600, which is our fraction 𝑏 over 𝑐, we can instead multiply by the reciprocal fraction 𝑐 over 𝑏, which in this case is 3600 divided by one.
Now 3600 divided by one is simply 3600. And so we have that our speed is given by 0.0025 multiplied by 3600 meters per hour. If we do this multiplication, we find that 0.0025 multiplied by 3600 gives us a value of nine. So the answer to the question is that the speed of the snail measured in units of meters per hour is equal to nine meters per hour.