Question

A sailor can row a boat 8 km downstream and return back to the starting point in 1 hr 40 min. if the speed of the stream is 2 km/hr find the speed of the boat in still water.

Answer 1

speed of the stream = 2 km/hr
let speed of the boat in still water be x km/hr

Time taken to travel downstream = 8/(x+2)
Time taken to travel upstream = 8/(x-2)

Total time = 1 hr 40 min = 5/3 hr
8
(
x
+
2
)
+
8
(
x
−
2
)
=
5
3
8(x+2)+8(x−2)=53

24(x- 2) + 24(x+2) = 5(x+2)(x-2)
48x = 5x2 - 20
5x2 - 48x -20=0

x =
48
±
√
(
−
48
)
2
−
4
×
5
×
(
−
20
)
2
×
5
48±(−48)2−4×5×(−20)2×5

=
48
±
√
2304
+
400
10
=48±2304+40010

=
48
±
52
10
=48±5210

= 10 (taking only the positive value)

i.e., speed of the boat in still water = 10 km/hr