SOLUTION: a boat was able to cover 90 kms. downstream in 3 hours. it was able to return to its original position in 4 1/2 hours. what was the speed of the boat and the speed of the curent?

Question 179897: a boat was able to cover 90 kms. downstream in 3 hours. it was able to return to its original position in 4 1/2 hours. what was the speed of the boat and the speed of the curent?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a boat was able to cover 90 km. downstream in 3 hours. it was able to return to its original position in 4 1/2 hours. what was the speed of the boat and the speed of the current?
:
Let s = speed of the boat in still water
let c = speed of the current
then we can say
(s+c) = speed down-stream
(s-c) = speed up-stream
;
Write a distance equation for each trip; dist = time * speed
;
3(s+c) = 90
4.5(s-c) = 90
:
Simplify both equations, divide the 1st eq by 3, and the 2nd eq by 4.5, results:
s + c = 30
s - c = 20
-------------addition eliminates c, find s
2s = 50
s = 25 km/hr speed of the boat in still water
;
Find c using s + c = 30
25 + c = 30
c = 30 - 25
c = 5 km/hr speed of the current
;
:
Check solution in the 2nd original equation:
4.5(s-c) = 90
4.5(25 - 5) =
4.5 * 20 = 90; confirms our solutions
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