Question

Alvin can go upstream at a rate of 15 miles per hour and downstream at a rate of 25 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 16 hours, how far did he travel on the river?

Answer 1

Answer:

Alvin traveled 150 miles downstream and 150 miles upstream, for a total distance on the river of 300 miles.

Step-by-step explanation:

Let d represent the distance Alvin traveled in one direction on the river. Then going downstream that distance took ...

... time = distance/speed

... time downstream = d/25

and the time going upstream that same distance to his point of origin took ...

... time upstream = d/15

The total of these times is 16 hours, so we have ...

... 16 = d/25 + d/15

Multiplying by 75 gives ...

... 1200 = 3d +5d = 8d

... 1200/8 = d = 150

Alving spent 6 hours going 150 miles downstream and 10 hours going 150 miles upstream. His total river distance was 300 miles. (We cannot tell which of these numbers will be considered to be the answer to the question.)