SOLUTION: a boat traveled downstream a distance of 72 mi and then came right back. If the speed of the current at 7 mph and the total trip took 3 hours, find the average speed of the boat re

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Question 786281: a boat traveled downstream a distance of 72 mi and then came right back. If the speed of the current at 7 mph and the total trip took 3 hours, find the average speed of the boat relative to the water
Answer by josgarithmetic(39632) About Me  (Show Source):
You can put this solution on YOUR website!
r = speed of boat without any river current

DIRECTION_________rate_____________time__________distance
down_____________r+7_______________(___)_________72
up_______________r-7_______________(___)_________72
Total________________________________3

Key concept among the numbers r%2At=d where r is rate, t is time, d is distance. Using this formula allows us t=d%2Fr


DIRECTION_________rate_______________time__________distance
down_____________r%2B7_______________72%2F%28r%2B7%29_________72
up_______________r-7_______________72%2F%28r-7%29_________72
Total_________________________________3


The time sum should be obvious. highlight%2872%2F%28r%2B7%29%2B72%2F%28r-7%29=3%29
Multiply left and right by %28r%2B7%29%28r-7%29, and THEN continue to simplify, finally solving for r.



Alternatively, 72%281%2F%28r%2B7%29%2B1%2F%28r-7%29%29=3
72%28%28r-7%2Br%2B7%29%2F%28r%5E2-49%29%29=3-------(maybe you could keep intermediate steps in+your+head+as+did+I%29
72%282r%29=3%28r%5E2-49%29
24%2A2r=r%5E2-49
r%5E2-48r-49=0
-Use general solution to quadratic formula-

r=98%2F2=49
Boat speed in still water, 49 mph.