Question

Two cities Mathura and Agra, 48 kms apart, are located on the bank of River Yamuna. A motor boat goes from Mathura to Agra and returns back as soon as possible. Yamuna flows at a speed of 6 km/hr. The motorboat completes the trip from Mathura to Agra and back in not more than 6 hours. Assuming the motorboat does not halt at Agra, what should be the minimum speed of motorboat in still water?
1. 16 km / hr
2. ​18 km / hr
3. 25 km / hr
4. 27 km / hr
5.

Answer 1

Correct Answer - Option 2 : ​18 km / hr

Calculation:

Let speed of boat = x km/hour

Speed of flow = 6 km/hour

Downstream speed = x + 6 km/hour

Upstream speed  = x - 6 km/hour

Given the distance between two cities = 48 km

According to given condition:

⇒ (48/x + 6) + (48/x - 6) ≤ 6

⇒ 48( x - 6) + 48( x + 6) ≤ 6 (x + 6) × (x - 6)

⇒ 48x - 288 + 48x + 288 ≤ 6(x² - 36)

⇒ 96x ≤ 6(x2 - 36)

⇒ 16x ≤ x2 - 36

⇒ 0 ≤ x2 - 16x - 36

By solving this equation we obtain:

⇒ x = 18

Hence the minimum speed of the motorboat in still water = 18 km/hour.

Distance is given by the formula, Distance = speed × time.

The direction along the stream is known as Downstream and the direction against the stream is known as Upstream.

Let the speed of the boat in still water  = x km/hour and the speed of stream = y km/hour

Downstream = (x + y) km/hour and Upstream = (x - y) km/hour.