SOLUTION: The current in a stream moves at a speed of 3km/h. A boat travels 40km upstream and 40km downstream in a total time of 14 hours. What is the speed of the boat in still water?

Question 2627: The current in a stream moves at a speed of 3km/h. A boat travels 40km upstream and 40km downstream in a total time of 14 hours. What is the speed of the boat in still water?
Answer by kiru_khandelwal(79) (Show Source): You can put this solution on YOUR website!
Let the speed of the boat be x km/h
speed of the stream = 3km/h
Upstream speed of the boat will be (x-3)km/h
and downstream speed of the boat will be (x+3)km/h
Distance travelled upstream = 40km
Distance travelled downstream = 40km
Time taked by the boat to go upstream = distance/speed = 40/(x-3)
Time taken by the boat to go downstream = distance/speed = 40/(x+3)
So Total time taken will be 40/(x-3) + 40/(x+3)
But the total time taken is 14 hrs
so the equation will be
40/(x-3) + 40/(x+3) = 14
=> (40(x+3) + 40(x-3))/(x+3)(x-3) = 14
=> 40(x+3+x-3)= 14(x+3)(x-3)
=> 40(2x) = 14(x^2 - 3^2)
=> 20(2x) = 7(x^2 -9)
=> 40x = 7x^2 -63
=> 7x^2 - 40x -63 =0
=> solve the equation for x to get the speed of the boat
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