SOLUTION: A motorboat maintained a constant speed of
24
24 miles per hour relative to the water in going
9
9 miles upstream and then returning. The total time for the trip was
1.0
1
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-> SOLUTION: A motorboat maintained a constant speed of
24
24 miles per hour relative to the water in going
9
9 miles upstream and then returning. The total time for the trip was
1.0
1
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Question 1147334: A motorboat maintained a constant speed of
24
24 miles per hour relative to the water in going
9
9 miles upstream and then returning. The total time for the trip was
1.0
1.0 hours. Use this information to find the speed of the current.
If the speed of the current is "x" miles per hour, then
- the effective rate of the motorboat upstream is (24-x) mph, while
- the effective rate of the motorboat downstream is (24+x) mph.
Then the time moving upstream is hours, while
the time moving downstream is hours.
The total time is 1 hour, giving you this "time" equation
+ = 1 hour.
To solve it, multiply both sides by (24-x)*(24+x). You will get
9*(24+x) + 9*(24-x) = .
Simplify step by step
9*24 + 9x + 9*24 - 9x = ,
2*9*24 = = = 24*(24-2*9) = 24*6 = 12*12 = .
It implies x = = 12.
ANSWER. The speed of the current is 12 miles per hour.
CHECK. + = + = + = 1 hour. ! Precisely correct !
Solved.
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It is a typical and standard Upstream and Downstream round trip word problem.
