SOLUTION: A boat can be rowed at 4 times the speed of the current. If the boater in travel 18 miles upstream in six hours and 10 miles downstream in two hours, how fast in miles per hour can

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Question 1180881: A boat can be rowed at 4 times the speed of the current. If the boater in travel 18 miles upstream in six hours and 10 miles downstream in two hours, how fast in miles per hour can the boat be rowed? Show your work
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
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A boat can be rowed at 4 times the speed of the current. If the boater in travel 18 miles upstream in six hours and 10 miles downstream in two hours, how fast in miles per hour can the boat be rowed?
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                 SPEED         TIME     DISTANCE

UPSTREAM          4c-c          6        18

DOWNSTRM          4c+c          2        10

Easiest to find c, speed of the current, then evaluate 4c for boast speed in absence of current.

2%284c%2Bc%29=10
4c%2Bc=5
5c=5
highlight_green%28c=1%29

Boat can be rowed highlight%284_miles_per_hour%29

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But upstream and downstream need to be able to match.
6%284c-c%29=18
3c=3
c=1
-
4c=4%2A1=4

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

If the boat can be rowed at 4 times the speed of the current, then its speed upstream is 4r - r = 3r,
where "r" is the rate of the current.



Then for "r" you have this distance equation

    6 hours * 3r mph = 18 miles, 

which gives the ANSWER  r = 18/(6*3) = 1 mph for the rate of the current and  4*1 = 4  mph for the rate of the boat in still water.



In this problem, ONLY ONE condition is necessary:  EITHER  for upstream travel  OR  for downstream travel.



To have these two conditions is UNNECESSARY and EXCESSIVE LUXURY in this problem.

Solved, answered and explained.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The upstream speed is the rate of the boat MINUS the speed of the current; the downstream speed is the rate of the boat PLUS the speed of the current.

The upstream speed is 18/6=3mph; the downstream speed is 10/2=5mph.

That means the rate of the boat is 4mph and the speed of the current is 1mph.

The information that the boat speed is 4 times the speed of the current is not needed in the problem.