SOLUTION: A motorboat maintain a constant speed of 15 mph in the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Find the speed of the water c
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Question 628799: A motorboat maintain a constant speed of 15 mph in the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Find the speed of the water current?
You can put this solution on YOUR website! A motorboat maintain a constant speed of 15 mph in the water in going 10 miles
upstream and then returning.
The total time for the trip was 1.5 hours.
Find the speed of the water current?
:
Let c = speed of the current
then
(15-c) = effective speed upstream
and
(15+c) = effective speed downstream
:
Write a time equation, time = dist/speed
;
time up + time back = 1.5 hrs + = 1.5
:
Multiply thru by (15-c)(15+c) to clear the denominators, results:
10(15+c) + 10(15-c) = 1.5(15+c)(15-c)
:
150 + 10c + 150 - 10c = 1.5(225-c^2)
300 = 337.5 - 1.5c^2
:
Add 1.5c^2 to both sides, subtract 300 from both sides
1.5c^2 = 337.5 - 300
1.5c^2 = 37.5
:
Divide both sides by 1.5
c^2 = 25
c =
c = 5 mph is the current
:
You can check this in the original time equation; replace with 5
