A motor boat whose speed in still water is 18 km/hr. takes 1 hour more to go 24 km up stream that to return downstream to the same spot. Find the speed of the stream. (CBSE 2018)

Given: Speed of boat = 18 km/h

Distance = 24 km

To find: speed of the stream

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x² and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

Given, motor boat whose speed in still water is 18 km/hr. takes 1 hour more to go 24 km up stream that to return downstream to the same spot.

Let the speed of stream be ‘a’ km/hr.

Relative speed of boat going upstream = 18 – a km/hr

Relative speed of boat going downstream = 18 + a km/hr

⇒ 24(18 + a – 18 + a) = -a² + 324

⇒ a² + 48a – 324 = 0

⇒ a² + 54a - 6a – 324 = 0

⇒ a (a + 54) – 6(a + 54) = 0

⇒ (a – 6) (a + 54) = 0

⇒ a = 6 and a = -54

As speed cannot be negative.

⇒ a = 6 km/hr.

Hence speed of the stream is 6 km/hr.