SOLUTION: A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the current.
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-> SOLUTION: A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the current.
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Question 1134504: A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the current. Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52803) (Show Source):
Let "c" be the speed of the current, in miles per hour.
Then the speed downstream is (16+c) miles per hour, while the speed upstream is (16-c) miles per hour.
The time traveling 15 miles downstream is hours.
The time traveling 9 miles upstream is hours.
From the condition, you have this "time" equation
= hours.
To solve it, multiply both sides by (16+c)*(9-c). You will get
15*(16-c) = 9*(16+c).
Simplify and solve:
15*16 - 15c = 9*16 + 9c
15*16 - 9*16 = 9c + 15c
6*16 = 24c
c = = = 4.
ANSWER. The currecnt speed is 4 miles per hour.
Solved.
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It is a typical and standard Upstream and Downstream trip word problem.
If the times are the same, then the ratio of distances is the same as the ratio of speeds.
Let c be the speed (mph) of the current. Since the boat's speed in still water is 16, the upstream and downstream speeds are 16-c and 16+c. Then, since the boat can go 15mi downstream in the same time is can go 9mi upstream,
