F.4 Maths

A boat travels against a stream flowing at 3km/h for 20 km and then returns to its starting point with the current. If the whole journey takes 7 hours, find the speed of the boat in the still water.
Take starting point as the lowest point,
Let x km/h be the speed of the boat in still water,
Going upward distance : 20km
Going upward speed : (x - 3)km/h
Going downward distance : 20km
Going downward speed : (x+3)km
Total time consumed : 7h
20/(x-3) + (20)/(x+3) = 7
(20)(x-3+x+3) = 7(x-3)(x+3)
20(2x) = 7x^2 - 63
7x^2 - 40x - 63 = 0
x = [40+/-√(1600+1764)]/14
x = 20/7 +/- 29/7
x = 49/7 or -9/7
x = 7 or -9/7
Since speed is always positive, x = 7 or -9/7(rej.)
Hence, the speed of the boat in still water - 7km/h

Let the speed of the boat in the still water is x km/h
Then the speed of the boat should be
(x-3) km/h (against the stream)
(x+3) km/h (follow the stream)

So, 20/(x-3)+20/(x+3)=7
20(x+3)+20(x-3)=7(x+3)(x-3)
40x=7x^2-63
7x^2-40x-63=0
(7x+9)(x-7)=0
x=-9/7 (rejected) or x=7

The speed of the boat in the still water is 7 km/h