Question 830597: If a boat travels from Town A to Town B, it has to travel 1501.5 mi along a river.
A boat traveled from Town A to Town B along the river’s current with its engine running at full speed. This trip took 71.5 hr.
Then the boat traveled back from Town B to Town A, again with the engine at full speed, but this time against the river’s current. This trip took 136.5 hr.
Write and solve a system of equations to answer the following questions.
The boat’s speed in still water with the engine running at full speed is?
The river current’s speed was?
I tried D/T=R for each. Then I'm stumped from there. I'm really unsure of how to set up this equation. If I could have some help as to how to set it up, I know I can solve it. Thank you!
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If a boat travels from Town A to Town B, it has to travel 1501.5 mi along a river.
A boat traveled from Town A to Town B along the river’s current with its engine running at full speed. This trip took 71.5 hr.
Then the boat traveled back from Town B to Town A, again with the engine at full speed, but this time against the river’s current. This trip took 136.5 hr.
:
Let s = boat speed in still water
Let c = rate of the current
then
(s+c) = effective speed downstream
and
(s-c) = effective speed upstream\
Write and solve a system of equations
write a distance equation for each way; dist = time * speed
:
71.5(s + c) = 1501.5
136.5(s - c) = 1501.5
:
They make it easy for you, simplify, divide the 1st equation by 71.5
Divide the 2nd equation by 136.5, leaving an easy elimination problem
s + c = 21
s - c = 11
--------------adding eliminates c, find s
2s = 32
s = 16 mph in still water
I'll let you find the current
Answer by josgarithmetic(39618)  (Show Source):
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