Question

A boat goes 24 km upstream and 28 km dowstream in 6 hours. If it goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes, find the speed of the stream.

• A. 10 km/hr
• B. 5 km/hr
• C. 4 km/hr
• D. 6 km/hr

Answer 1

Answer: (C)

4 km/hr

Answer 2

Assume the speed of boat be $x\ \frac{km}{hr}$

the speed of boat be stream $y\ \frac{km}{hr}$

The speed in Downstream = $(x + y) \frac{km}{hr}$

The speed in Upstream $(x - y) \frac{km}{hr}$

Given in the question,

$\frac{24}{x - y} + \frac{28}{x + y} = 6$ – (i)

$\frac{30}{x - y} + \frac{21}{x + y} = 6.5$ – (ii)

By multiplying equation (i) with -3 and equation (ii) with 4 we get,

$\frac{48}{x - y} = 26 - 18$

$x - y = \frac{48}{8} = 6$ – (iii)

$x + y = 14$ – (iv)

Subtracting equation (iii) from equation (iv) we get,

$y = \frac{8}{2} = 4$

The correct option is (C): 4 km/hr