SOLUTION: Your fishing boat moves at 12 miles per hour relative to the surrounding water. You ride it from your house up the Mississippi River to a point that’s 16 miles distant, and then re

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Question 580159: Your fishing boat moves at 12 miles per hour relative to the surrounding water. You ride it from your house up the Mississippi River to a point that’s 16 miles distant, and then return to your house. The round trip takes 4 hours. The speed of the river is
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Your fishing boat moves at 12 miles per hour relative to the surrounding water.
You ride it from your house up the Mississippi River to a point that’s 16 miles distant, and then return to your house.
The round trip takes 4 hours. The speed of the river is
:
Let c = the speed of the river
then
(12-c) = effective speed up-river
and
(12+c) = effective speed down river
:
write a time equation; time = dist/speed
:
Upriver time + downriver time = 4 hrs
16%2F%28%2812-c%29%29 + 16%2F%28%2812%2Bc%29%29 = 4
;
multiply by (12-c)(12+c), gets rid of the denominators and we have:
16(12+c) + 16(12-c) = 4(12+c)(12-c)
;
192 + 16c + 192 - 16c = 4(144-c^2)
:
384 = 576 - 4c^2
:
4c^2 = 576 - 384
4c^2 = 192
c^2 = 192/4
c^2 = 48
c = sqrt%2848%29
c = 6.9282 ~ 6.9 mph is the speed of the river
:
:
See if that checks out
16%2F%28%2812-6.9%29%29 + 16%2F%28%2812%2B6.9%29%29
3.137 + .847 = 3.984 ~ 4 hrs