SOLUTION: A motorboat travels 200 kilometers in 4 hours going upstream and 294 kilometers in 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the
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Question 1172595: A motorboat travels 200 kilometers in 4 hours going upstream and 294 kilometers in 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
You can put this solution on YOUR website! A motorboat travels 200 kilometers in 4 hours going upstream and 294 kilometers in 3 hours going downstream.
What is the rate of the boat in still water and what is the rate of the current?
:
let s = the rate of the boat in still water
let c = the rate of the current
then
(s-c) = effective rate upstream
(c+c) = effective rate downstream
:
Write a distance equation for each way (dist = time * rate)
4(s-c) = 200
3(s+c) = 294
We can simplify both these equation, divide the 1st by 4, the 2nd by 3
s - c = 50
s + c = 98
----------------Addition eliminates c, find s
2s + 0 = 148
s = 148/2
s = 74 km/hr is the speed in still water
then using s + c = 98
74 + c = 98
c = 98 - 74
c = 24 km/hr is the rate of the current
:
:
Confirm this in the first original equation
4(74-24) =
4(50) = 200
