SOLUTION: A boat went 10km upstream against the current then turned around and went 15km downstream with current. The current speed was 3km/hour and upstream trip took 30 minutes longer. Wha
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Question 325322: A boat went 10km upstream against the current then turned around and went 15km downstream with current. The current speed was 3km/hour and upstream trip took 30 minutes longer. What was the speed of the boat without the speed of the current?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
10km upstream against the current
15km downstream with current.
current speed was 3km/hour
upstream trip took 30 minutes longer.
..
let speed in still water be x km/hour
..
downstream speed = x+3 km/hour
15 km distance.
time taken = 15/ x+3
..
upstream speed will be x-3 km/hour
distance 10 km.
time taken = 10/x-3
..
upstream time - downstream time = 1/2 hour
10/ x-3 - 15/ x+3 =1/2
LCM of left side
(x+3)(x-3)
10(x+3)-15(x-3)/ (x+3)(x-3)= 1/2
10x+30-15x+45=1/2 * (x+3)(x-3)
-5x+75= 1/2 * x^2-9
2(-5x+75)=x^2-9
-10x+150=x^2-9
x^2+10x-159=0
..
the roots of the equation x1 , x2 will be
x1= (-10+sqrt(100+636) )/2
x1=-18.56 since it is negative ignore.
x2=(-10-sqrt(100+636) )/2
x2= 8.56 km/hr the speed of boat in still water
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