Find the speed of a helicopter flying at 187 miles per hour. Give the answer in miles per second to two decimal places.
The question says to find the speed of the helicopter. Well, 187 miles per hour is the speed of the helicopter. But we’re not interested in how many miles it can fly in an hour. We need to know its speed in miles per second. We’ll start with what we’re given, 187 miles per hour. In the end, we’ll need to know how many miles this helicopter can go in one second. This means that we have the correct units in our numerator and we need to focus on the units in our denominator.
Since we have hours in the denominator, we’ll need to get rid of that by having hours in the numerator. We don’t usually memorize how many seconds are in one hour, so we can’t go from one hour to seconds. We do know that one hour equals 60 minutes, so we can start there. We’ll multiply 187 miles per hour by one hour over 60 minutes. It’s important to notice here that we are multiplying the speed by one. One hour equals 60 minutes. We’re using this to change the units, but we haven’t changed the speed that the helicopter is travelling.
Now, we’ve gotten rid of the hour units. We now have miles per minute. We have minute in the denominator, so we’ll need minutes in the numerator. We do memorize how many seconds are in a minute. One minute equals 60 seconds. Again, we’re multiplying by one. The minutes in the denominator and the minutes in the numerator cancel out. In the numerator, we have 187 times one times one miles, 187 miles. In the denominator, we have 60 times 60 seconds. And so, we know the helicopter is travelling 187 miles every 3600 seconds.
But we want to know how many miles the helicopter is travelling in one second. To go from 3600 seconds to one second in the denominator, we need to divide by 3600. And if we divide by 3600 in the denominator, we need to divide by 3600 in the numerator. When we do that, we get 0.05194 repeating, which tells us that the helicopter is travelling at 0.05194 repeating miles per second.
To solve this correct to two decimal places, we look at the second decimal place, where we have a five. To the right of that five is a one. This means we’ll round down to 0.05. And our units are miles per second. Which tells us that this helicopter was travelling five hundredths of a mile per second. This is a very expanded way of solving the problem. You could take 187 miles in one hour divide by 60 to get miles per minute and then divide by 60 again to get miles per second. Both ways will yield 0.05 miles in one second.