(Q13) A motor boat heads upstream a distance of 24km on a river whose current is running at 3 km per hour. The trip up and back takes 6 hours. Assuming that the motor boat maintained a constant speed, what was its speed?

Answer

Let the speed of the boat in still water be x kmph.

Speed of the current = 3 kmph

Then speed of the boat in upstream = (x - 3) kmph

Speed of the boat in downstream = (x + 3) kmph

By problem total time taken = 6h.

∴
24
x - 3
 +
24
x + 3
 = 6
24[
1
x - 3
 +
1
x + 3
] = 6
24[
x + 3 + x - 3
(x + 3)(x - 3)
] = 6

24(2x) = 6(x2 - 9)

8x = x2 - 9

x2 - 8x - 9 = 0

x2 - x + x-9 = 0

x(x - ) + 1(x - ) = 6

(x - )(x + 1) = 0

x- = 0 or x + 1 = 0

x can't be negative,

∴ x =

speed of the boat in still water = kmph