Alvin can go upstream at a rate of 4.8 miles per hour and downstream at a rate of 8.5 miles per hour. One day while Alvin was on the river, he received a call telling him he need to turn around and come home. So he turned around and went back to his starting point. If his entire trip took 17 hours, how far did he travel on the river?

Question

mathstudent55 · Answer

Distance each way: d
upstream: speed 4.8 mph, time t1
downstream: speed 8.5 mph, time t2
Total time: 17 h

distance = speed * time

upstream
d = 4.8 * t1

downstream
d = 8.5 * t2

t1 + t2 = 17
t1 = 17 - t2

d = 4.8(17 - t2)
d = 8.5(t2)

4.8(17 - t2) = 8.5t2
81.6 - 4.8t2 = 8.5t2
81.6 = 13.3t2
t2 = 6.135 h

d = 8.5 * t2 = 8.5 * 6.135 = 52.15 miles

anonymous · Answer

thank you this really helped i get what you did and i was able to do two other similar questions

mathstudent55 · Answer

Great. you're welcome.

anonymous · Answer

Refer to a solution using the Mathematica computer program.