# The time required to drive a certain distance varies inversely as the speed. If it takes 4 hours to drive the distance at 40 mph, how long will it take to drive the distance at 50 mph?

##### 1 Answer

It will take

#### Explanation:

You can solve this problem by using the fact that speed and time have an *inverse relationship*, which means that when one **increases**, the other *decreases*, and vice versa.

In other words, speed is *directly proportional* to the **inverse** of the time

You can use the *rule of three* to find the time needed to travel that distance at 50 mph - remember to use the inverse of time!

Now cross-multiply to get

**Alternatively**, you can use the fact that distance is defined as the product between speed and time

SInce the distance is the same in both cases, you can write

Once again,