SOLUTION: A motorboat maintained a constant speed of 11 miles per hour relative to water in Goin 30 miles upstream and then returning. The total time for the trip was 5.5 hours. Use this inf

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Question 471491: A motorboat maintained a constant speed of 11 miles per hour relative to water in Goin 30 miles upstream and then returning. The total time for the trip was 5.5 hours. Use this information to find the speed of the current


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat maintained a constant speed of 11 miles per hour relative to water in Going 30 miles upstream and then returning.
The total time for the trip was 5.5 hours.
:
Let c = speed of the current
then
(11+c) = speed downstream relative to land
and
(11-c) = speed upstream relative to the land
:
Write a time equation: time = dist/speed
:
time upstream + time downstream = 5.5 hrs
30%2F%28%2811-c%29%29 + 30%2F%28%2811%2Bc%29%29 = 5.5
:
Multiply by (11-c)(11+c), results:
30(11+c) + 30(11-c) = 5.5(11+c)(11-c)
:
330 + 30c + 330 - 30c = 5.5(121 - 11c + 11c - c^2)
:
660 = 5.5(121 - c^2)
:
660 = 665.5 - 5.5c^2
:
5.5c^2 = 665.5 - 660
:
5.5c^2 = 5.5
Divide both sides by 5.5
c^2 = 1
c = 1 mph is the current
:
:
See if this is true; find the times both ways
downstream: 30/12 = 2.5 hrs
up-stream: 30/10 = 3.0 hrs
----------------
total time: 5.5 hrs