Question

The speed of a boat in still water is 5 km/hr. If it takes thrice as much time in going 20 km upstream as in going the same distance downstream, find the speed of the stream:

• A. 5.5 km/hr
• B. 2.5 km/hr
• C. 6.5 km/hr
• D. 15.5 km/hr
• E. 3.5 km/hr

Hint:

Upstream speed = still water speed - stream speed; Downstream speed = still water speed + stream speed.

Answer 1

The Correct Option is B

Step 1: Defining Variables:
Let speed of stream = \(x\) km/hr.
Downstream speed = \(5 + x\) km/hr.
Upstream speed = \(5 - x\) km/hr.

Step 2: Time Relationship:
Time upstream = 3 × Time downstream
\[ \frac{20}{5 - x} = 3 \times \frac{20}{5 + x} \]
Cancel 20:
\[ \frac{1}{5 - x} = \frac{3}{5 + x} \]

Step 3: Solving:
\[ 5 + x = 3(5 - x) \]
\[ 5 + x = 15 - 3x \]
\[ x + 3x = 15 - 5 \]
\[ 4x = 10 \]
\[ x = 2.5 \text{ km/hr} \]