# You ride your bike to campus a distance of 8 miles and return home on the same route. Going to campus, you ride mostly downhill and average 5 miles per hour faster than on your return trip home. Continued in details?

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If the round trip takes two hours and 24 minutes—that is, 12/5 hours—what is your average rate on the return trip?

If the round trip takes two hours and 24 minutes—that is, 12/5 hours—what is your average rate on the return trip?

##### 1 Answer

#### Explanation:

We know that Rate

Therefore, Time = Distance

We can also create two equations to solve for the rate: one for to campus and one for coming back home.

**TO FIND THE AVERAGE RATES**

Let

If we define

**TO CREATE AN EQUATION**

We know that both trips were 8 miles. Therefore, Distance

In the above equation, I added the time (Distance

**TO SOLVE THE EQUATION**

Multiply the whole equation through by the LCM (the product of all the denominators in this case)