Question

It took Brian 8 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 9 mph and make thereturn drive in only 7 hours. Find his average speed on the return drive.Step 1 of 3: Complete the following table by entering the missing values, using x to represent the unknown quantity.

Answer 1

In the row of "original drive", we have the first part of the travel, so the time needed was 8 hours. The distance can be found by multiplying the rate and the time:

`\begin{gathered} \text{distance}=\text{rate}\cdot\text{time} \\ \text{distance}=x\cdot8=8x \end{gathered}`

Then, in the "return drive", the rate is 9 mph higher, so the rate is "x + 9".

Also, the time is 7 hours. So, the distance is:

`\text{distance}=(x+9)\cdot7=7x+63`

Since the distances are the same, we can write the following equation and solve it for x:

`\begin{gathered} 8x=7x+63 \\ 8x-7x=63 \\ x=63 \\ \\ x+9=63+9=72\text{ mph} \end{gathered}`

Therefore the average speed on the return drive is 72 mph.