A motorboat whose speed is 18 km/h in still water takes 1 hr 30 minutes more to go 36 km upstream than to return downstream to the same spot. Find the speed of the stream.

Given: Speed of the boat = 18km/hr

Let speed of stream be x km/hr

Speed of boat in upstream = (18 – x)km/hr

Speed of boat in downstream = (18 + x)km/hr

We know that,

According to question,

Time taken to travel upstream

- time taken to travel downstream = 1hr 30 minutes

⇒ 2[36(18 + x – 18 + x] = 3[(18)² – (x)²]

[∵ (a – b)(a + b) = (a² – b²)]

⇒ 2[36(2x)] = 3[324 – x²]

⇒ 144x = 972 – 3x²

⇒ 3x² + 144x – 972 = 0

⇒ x² + 48x – 324 = 0

Comparing eq. with ax² + bx + c = 0

Here a = 1, b = 48 and c = -324

We know that,

D = b² – 4ac

= (48)² – 4(1)(-324)

= 2304 + 1296

= 3600

So, the roots to the equation are

x = -24 ± 30

⇒ x = -24 + 30 or x = -24 – 30

⇒ x = 6 or x = -54

Since, x is the speed, so it can’t be negative

So, x = 6 km /hr