SOLUTION: A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstrem to a certain point in 20 minutes, the return trip takes 15 minu

Question 266575: A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstrem to a certain point in 20 minutes, the return trip takes 15 minutes. What is the speed of the current?
Thanks for any help you can provide,
orchidia@tampabay.rr.com

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A motorboat can maintain a constant speed of 16 miles per hour relative to the water.
The boat makes a trip upstream to a certain point in 20 minutes, the return trip takes 15 minutes.
What is the speed of the current?
:
Change 20 min to hr
Change 15 min to hr
:
Let c = rate of the current
then
(16-c) = rate upstream
and
(16+c) = rate downstream
:
Assume the trip up and the trip back were the same distance
Write a distance equation: dist = time * rate
:
Dist upstream = dist downstream
(16+c) = (16-c)
Multiply both sides by 12, to get rid of the denominators, results:
3(16+c) = 4(16-c)
48 + 3c = 64 - 4c
3c + 4c = 64 - 48
7c = 16
c =
c = 2.2857 mph is the current
:
:
Check solution by finding the distance of each trip (should be equal)
.25(16+2.2857) = 4.57 mi
.333(16-2.2857) = 4.57 mi
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