Question

Question 11 > Alvin can go upstream at a rate of 25 miles per hour and downstream at a rate of 35 miles per hour. One day while Alvin was on the river, he received a call telling him he needs to turn around and come home. So he turned around and went back to his starting point. If his entire trip took 12 hours, how far did he travel on the river? Alvin traveled miles. (Roundtrip) Question Help: Message instructor Submit Question

Answer 1

Given Data:

The upstream speed is, 25 miles/hr.

The downstream speed is, 35 miles/hr.

The total time is, 12 hr.

Let d be the distance traveled. He can travel 25 miles/ hr in upstream, so the time taken will be,

`t=(d)/(25)`

He can travel 35 miles/ hr in upstream, so the time taken will be,

`t^(\prime)=(d)/(35)`

Total time is, 12 hr. So we have,

`\begin{gathered} 12=(d)/(25)+(d)/(35) \\ 12=(d)/(5*5)+(d)/(7*5) \\ 12=(1)/(5)((d)/(7)+(d)/(5)) \\ 12*5=(d)/(7)+(d)/(5) \\ 60*35=5d+7d \\ 2100=12d \\ d=(2100)/(12)=175 \end{gathered}`

Therefore the total distance is, 350 mile