Question

If there are 5280 feet in a mile and 3600 seconds in an hour, determine the runners speed in miles per hour. Round to the nearest tenth and show work

Answer 1

Part a) The runner is travelling at
`20\ (ft)/(sec)`

Part b) The runner's speed is
`13.6\ (mi)/(h)`

Explanation:

The complete question in the attached figure

Part a) we know that

The speed is equal to divide the distance by the time

Let

s ----> the speed

x ----> the distance

y ---> the time

`s=(x)/(y)`

we have

`x=100\ yd\\y=15\ sec`

Remember that

`1\ yd=3\ ft`

Convert yards to feet

`x=100\ yd=100(3)=300\ ft`

Find the speed

`s=(300)/(15)`

`s=20\ (ft)/(sec)`

Part b) we know that

`1\ mi=5,280\ ft`

`1\ h=3,600\ sec`

we have

`x=300\ ft`

`y=15\ sec`

Convert feet to miles

`x=300\ ft=300/5,280\ mi`

Convert seconds to hours

`y=15\ sec=15/3,600\ h`

substitute

`s=(x)/(y)`

`s=((300/5,280))/((15/3,600))`

`s=(300*3,600)/(5,280*15)=(1,080,000)/(79,200)=13.6\ (mi)/(h)`