Answer :

**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 x^{2} 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) = -a^{2} + 324

⇒ a^{2} + 48a – 324 = 0

⇒ a^{2} + 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.**

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