SOLUTION: A river boat can head 340 miles up-river in 19 hours, but the return trip takes only 14 hours. Find the current of the river and find the speed of the ship in still water to the ne

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Question 61354: A river boat can head 340 miles up-river in 19 hours, but the return trip takes only 14 hours. Find the current of the river and find the speed of the ship in still water to the nearest tenth of a mph.
(Should X equal the speed of the ship? Or the current of the river? Or both?) Okay I am stuck any help would be greatly appreciated. Thank-You.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
A river boat can head 340 miles up-river in 19 hours, but the return trip takes only 14 hours. Find the current of the river and find the speed of the ship in still water to the nearest tenth of a mph.
:
The distance formula is:highlight%28d=rt%29, d=distance, r=rate, t=time
:
Let x=speed of the boat
let c=speed of the current
:
The rate upstream is: x-c
time upstream is: 19 hrs
The rate down stream is: x+c
time downstream is: 14
Distance for both is: 340 mi
:
The equation for upstream is:
19(x-c)=340
The equation for down stream is:
14(x+c)=340
:
Solve one of the equations for c and substitute it into the other and solve for x.
19x-19c=340
-19x+19x-19c=-19x+340
-19c=-19x+340
-19c%2F-19=%28-19x%2B340%29%2F-19
c=x%2B%28340%29%2F-19
:
14%28x%2Bhighlight%28x%2B%28340%29%2F-19%29%29=340
14%282x-340%2F19%29=340
28x-250.5263158=340
28x-250.5263158%2B250.5263158=340%2B250.5263158
28x=590.5263158
28x%2F28=590.5263158%2F28
x=21.1
The boat would be going 21.1 mph in still water.
Happy Calculating!!!