SOLUTION: Kyle is planning a 3 hour trip down a river and back to his starting point. He knows he can paddle in still water at 3 mph and that the rate of the current is 2 mph. How much time

Question 963134: Kyle is planning a 3 hour trip down a river and back to his starting point. He knows he can paddle in still water at 3 mph and that the rate of the current is 2 mph. How much time can he spend going downstream? How far downstream can he travel?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Let d=distance one way; p=paddle rate still=3mph; c=current rate=2mph
time downriver+time upriver=3 hours
d/(p+c)+d/(p-c)=3 hours
d/(3mph+2mph)+d/3mph-2mph)=3 hours
d/5mph+d/1mph=3 hours
(1/5)d+d=3 hours
6/5d=3hours Multiply each side by 5/6
d=15/6 mi=2.5 miles ANSWER 1: Kyle can travel 2.5 miles downstream.
2.5 miles/p+c=time downstream
2.5mi/3mph+2mph=time downstream
2.5mi/5mph=time downstream
0.5 hour=time downstream ANSWER 2: Kyle can travel downstream for 1/2 hour.
CHECK:
Time downstream + Time upstream = 3 hours
0.5 hours+2.5mi/(3mph-2mph)= 3 hours
0.5 hours + 2.5 mi/1mph = 3 hours
0.5 hours + 2.5 hours = 3 hours
3 hours=3 hours

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