Question

7. The speed of a motor-boat in still water is
18 km/h. To travel 24 km downstream it takes
1 hour less than the time taken to cover the
same distance upstream. Find the speed of
the flow of the river.​

Answer 1

Given parameters:

The speed of the motorboat in still water =18 kmph

Let us consider

The speed of the stream = s

Speed of boat upstream = Speed of a boat in still water – the speed of a stream

Speed of boat upstream = 18 – s

Speed of boat downstream = Speed of a boat in still water + speed of a stream

Speed of boat downstream = 18 + s

Time is taken for upstream = Time taken to cover downstream + 1

time =distance/speed

24/ (18 – s) = [24/(18 + s)] + 1

24(18+s) = 24(18−s) + (18−s)(18+s)

s2 + 48s − 324 = 0

s2 + 54s − 6s − 324 = 0

(s+54)(s−6) = 0

s = 6,−54 but

s ≠−54

Since the speed of steam cannot be negative.

∴ s = 6km/hr