Question

A motor boat covers 16 km in 2 hours downstream and 14 km in 2 hours upstream. The speed of the motor boat is:

• A. 0.5 km/hr
• B. 5 km/hr
• C. 8 km/hr
• D. 7.5 km/hr

Answer 1

The Correct Option is D

To find the speed of the motorboat in still water, we first need to determine the speed of the boat downstream and upstream. Let's denote:

• The speed of the boat in still water as b km/hr.
• The speed of the current as c km/hr.

For downstream travel (with the current), the effective speed is (b + c) km/hr, and for upstream travel (against the current), it is (b - c) km/hr.

1. Downstream: Distance = 16 km, Time = 2 hours.

The speed downstream = Distance / Time = 16 km / 2 hr = 8 km/hr.

2. Upstream: Distance = 14 km, Time = 2 hours.

The speed upstream = Distance / Time = 14 km / 2 hr = 7 km/hr.

Using these equations:

• b + c = 8
• b - c = 7

Adding these two equations, we get:

(b + c) + (b - c) = 8 + 7

2b = 15

Therefore, b = 15/2 = 7.5 km/hr.

Hence, the speed of the motorboat in still water is 7.5 km/hr.