Question

A family goes on vacation to a water park. During the drive to the water park the weather caused thefamily to average 40 miles per hours. After their vacation the weather improved, so they could average 50miles per hour on the return trip. If the distance each way was equal, and the entire time driving was 9hours, find the distance one way to the water park.The distance the family travel one way to the water park wasmiles.Question Help Mer

Answer 1

Given, the speed in the first trip, S1=40 miles/h.

The speed in the return trip, S2=50 miles/h.

The distance is the same for both trips.

When the distance is same, the average speed of the drive is,

`\begin{gathered} S=(2S1S2)/(S1+S2) \\ =(2*40*50)/(40+50) \\ =(4000)/(90) \\ =(400)/(9)\text{ miles/h} \end{gathered}`

Given, the time taken for entire trip is t=9 h.

Now, the distance travelled both ways to park is,

`\begin{gathered} D=St \\ =(400)/(9)*9 \\ =400\text{ miles} \end{gathered}`

Hence, the distance travelled one way to the park is,

`\begin{gathered} d=(D)/(2) \\ =(400)/(2) \\ =200\text{ miles} \end{gathered}`

Therefore, the distance travelled one way to the park is 200 miles.