## Doing the Math

It’s not often you have to know how to convert inches per second to miles per hour. So while there is a general conversion, it’s better to know how to arrive at the answer mathematically. Let’s reason through this problem.

Say we are given a value of **30 inches per second**, and we need to convert it to miles per hour (mph). The best way to set up this kind of problem is to do some cross multiplication. So let’s write out our starting value in a fractional form: **30 inches/1 second**.

Now we need to figure out what to multiply this value by in order to arrive at mph. Remember, you can multiply your starting value by any fraction that is equal to 1. Since there are 3600 seconds in one hour (60 minutes per hour x 60 seconds per minute), we’ll multiply our starting value by **3600 seconds/1 hour**. This will convert the unit of our value from seconds to hours.

We also need to convert it to miles. There are 5,280 feet in a mile (this is a handy conversion to know) and 12 inches in a foot. 5,280 x 12 = 63,360 –and that’s how many inches there are in a mile. So we’ll also multiply our starting value by **1 mile/63360 inches**, which will convert the unit of our value from inches to miles.

Here’s how this calculation works:

## Getting the Answer

Notice that we can cross out both the “inches” and “seconds” labels, leaving our answer with the right units. Now all we have to do is perform the actual calculation. (30 x 3600) / 63360 = approximately 1.70, so our answer is **1.70 mph**.

If you plug in 1 inch per second for the first value, you’ll get a conversion factor of **1/17.6** or approximately **.0568**. So as a shortcut (and if you remember or memorize the conversion), you can simply multiply your inches per second value by .0568. For example, 30 inches per second x .0568 = 1.704 mph.

## Sample Problems

Here are some sample problems to help you practice how to convert inches per second to miles per hour.

**1. **While doing a physics experiment, Rob measures his cart’s speed to be 146 inches per second. What is the cart’s speed in miles per hour?

**2. **Belinda, who is doing the same physics experiment, is measuring her cart’s speed in 5 second intervals. If her cart moves 830 inches in 5 seconds, what is its speed in miles per hour?

**3. **The speed limit on a certain interstate is 65 miles per hour. How fast is this in inches per second? (This will require you to do the conversion backwards.)