Question

In a river running at 2 kmph, a motorboat goes 10 km upstream and back again to the starting point in 55 min, find the speed of the motorboat in still water.
1. 25 kmph
2. 20 kmph
3. 22 kmph
4. 30 kmph

Answer 1

Correct Answer - Option 3 : 22 kmph

Given:

Speed of River = 2 kmph

Distance upstream = 10 km

Time taken = 55 min

Formula Used:

Distance = T (x² – y²)/ 2x

Calculations:

Let Speed of motorboat in still water be x

Speed of stream (y) = 2 kmph

Time (T) = 55 min = 55/60 h

According to the formula,

Distance = T (x² – y²)/ 2x

⇒ 10 = 55/60 × (x² – y²)/ 2x

⇒ 240x = 11(x² – 4)

⇒ 11x² – 240x – 44 = 0

⇒ (x - 22) (11x + 2) = 0

Ignoring the negative value, we get

⇒ x = 22 kmph

∴ The speed of the motorboat in still water is 22 kmph.