Question

Speed of a boat in still water is 9km/hr. It goes 12 km down stream and comes back to the starting point in three hours. What is the speed of water in the stream?

• A. 3 km/hr
• B. 4 km/hr
• C. 4.5 km/hr
• D. 5 km/hr

Answer 1

Answer:

A. 3 km/hr

The speed of water in the stream is 3 km/hr.

1. Given Data:

• Speed of the boat in still water x = 9 km/hr

• Distance (d) = 12 km

• Total round-trip time = 3 hours

• Let the speed of the stream be y km/hr.

2. Formulate the Speeds:

• Downstream Speed = 9 + y km/hr

• Upstream Speed = 9- y km/hr

3. Set up the Time Equation:
$\text{Time\ Downstream}+\text{Time\ Upstream}=\text{Total\ Time}$
$\frac{12}{9+y}+\frac{12}{9-y}=3$

4. Solve for y:
Divide the entire equation by 3 to simplify:
$\frac{4}{9+y}+\frac{4}{9-y}=1$

Take a common denominator:
$\frac{4(9-y)+4(9+y)}{(9+y)(9-y)}=1$
$\frac{36-4y+36+4y}{9^{2}-y^{2}}=1$
$\frac{72}{81-y^{2}}=1$

Cross-multiply:
$72=81-y^{2}$
$y^{2}=81-72$

$y^{2}=9$
$y=\sqrt{9}=\mathbf{3}\text{\ km/hr}$