Question

7.24. If you walk for 45 minutes at a rate of 4 \mathrm{mph}$ and then run for 30 minutes at a rate of 10 mph, then how many miles have you gone at the end of one hour and 15 minutes? What was your average speed for the journey?

Answer 1

I would say It would be 6.4 mph

Answer 2

The average speed for the journey is 6.4 mph.

Explanation:

Given:

If you walk for 45 minutes at a rate of
`$4 \mathrm{mph}$` and then run for 30 minutes at a rate of
`$10 \mathrm{mph}$`, then how many miles have you gone at the end of one hour and 15 minutes Find the average speed for the journey

Step 1 of 1

We can compute the walking distance and running distances separately, then add them.

You walk for 45 minutes, which is
`(3)/(4)$` hours, at a rate of
`$4 \mathrm{mph}$`, so the walking distance is
`(4 \mathrm{mph})\left((3)/(4)\right.$ hours $)=3$` miles. You run for 30 minutes, which is
`(1)/(2)$ hour, at a rate of $10 \mathrm{mph}$`, so the running distance is
`$(10 \mathrm{mph})\left((1)/(2) h o u r\right)=5$` miles.

So the total distance you cover is 3+5=8 miles.

Now we can also compute the average speed for the journey.

You covered 8 miles in
`$(5)/(4)$` hours, so your average speed was

`$$\begin{aligned}&\frac{8 \text { miles }}{(5)/(4) \text { hours }}=(8)/((5)/(4)) \mathrm{mph} \\&(32)/(5) \mathrm{mph}=6.4 \mathrm{mph}\end{aligned}$$`