SOLUTION:
Meg rowed her boat upstream a distance of 15 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 7 mph, fi
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Meg rowed her boat upstream a distance of 15 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 7 mph, fi
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Question 1145947:
Meg rowed her boat upstream a distance of 15 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 7 mph, find the average speed of the boat relative to the water. Answer by ikleyn(52788) (Show Source):
Let "x" be the average speed of the boat relative to the water (usually called as a "boat speed in still water"), in miles per hour.
Then the speed of the boat downstream is (x+7) mph, and the time traveling 48 miles downstream is hours.
The speed of the boat upstream is (x-4) mph, and the time traveling 48 miles upstream is hours.
Total time for the round trip is 16 hours (given !), which gives you the "time" equation
+ = 16 hours. (1)
It is your basic equation to solve.
Multiply equation (1) by (x-7)*(x+7) = . You will get
15*(x+7) + 15*(x-7) = 16*(x^2-49).
Simplify it step by step.
15x + 15*7 + 15x - 15*49 = 16x^2 - 784
16x^2 - 30x - 784 = 0.
Apply the quadratic formula
= = .
Only positive root x = = 8 makes sense.
Answer. The boat speed in still water is 8 miles per hour.
CHECK. Let's check equation (1). Its left side is
+ = + = 15 + 1 = 16 hours - same as the given total time. ! The solution is correct !
Solved.
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It is very standard and typical round trip upstream and downstream Travel and Distance problem.
Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn how to solve this type of problems once and for all.
