A boat takes 1 hour 30 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 km/hr, then the speed of the stream is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2 km/hr
Let the speed of the stream be x km/hr. Then the downstream speed is 10 + x and the upstream speed is 10 − x. Since 1 hour 30 minutes = 3/2 hours,
\( \displaystyle \frac{36}{10 - x} - \frac{36}{10 + x} = \frac{3}{2} \)
\( \displaystyle \frac{36 \times 2x}{100 - x^2} = \frac{3}{2} \)
\(144x = 300 - 3x^2\)
\(x^2 + 48x - 100 = 0\)
\((x + 50)(x - 2) = 0\)
A speed cannot be negative, so x = 2 km/hr.
Shortcut: Try x = 2: upstream speed 8 km/hr, downstream speed 12 km/hr, and 36/8 − 36/12 = 4.5 − 3 = 1.5 hours, as required.