Question

The speed of a boat in still water is 20 km per hour. it goes 96 km upstream and written down to starting point in 10 hours. find the speed of the stream

Answer 1

Let the speed of the stream be 'x' km/hr.

Given that speed of the boat in still water is 20 km/hr.

(i)

Speed of the boat upstream = (20 - x) km/hr.

We know that : Time = Distance/Speed = 96/(20 - x)

(ii)

Speed of the boat downstream = (20 + x) km/hr

We know that Time : Distance/Speed = 96/(20 + x).

Now,

Time taken for upstream journey + Time taken for downstream journey = 10

⇒ (96/20 - x) + (96/20 + x) = 10

⇒ 96(20 + x) + 96(20 - x) = 10(20 + x)(20 - x)

⇒ 1920 + 96x + 1920 - 96x = 10(20^2 - x^2)

⇒ 3840 = 4000 - 10x^2

⇒ -160 = -10x^2

⇒ x^2 = 16

⇒ x = 4, -4{Speed cannot be negative}

⇒ x = 4.

Therefore, Speed of the stream is 4 km/hr.

Hope it helps!