Single correct option
A boat covers 24 km upstream and 36 km downstream in 6 hours. It covers 36 km upstream and 24 km downstream in 6.5 hours. What is the speed of the stream (in km/h)?
- A. 1.5
- B. 2
- C. 2.5
- D. 3
Show answer and solution
Answer: (B) 2
Let u = 1/(upstream speed) and d = 1/(downstream speed).
24u + 36d = 6 … (i)
36u + 24d = 6.5 … (ii)
Multiply (i) by 3 and (ii) by 2: 72u + 108d = 18 and 72u + 48d = 13. Subtracting: 60d = 5 ⇒ d = 1/12, so downstream speed = 12 km/h.
Then 24u = 6 − 36/12 = 3 ⇒ u = 1/8, upstream speed = 8 km/h.
Stream speed = (12 − 8)/2 = 2 km/h (boat in still water = 10 km/h).
Check: 24/8 + 36/12 = 3 + 3 = 6 ✓; 36/8 + 24/12 = 4.5 + 2 = 6.5 ✓.
24u + 36d = 6 … (i)
36u + 24d = 6.5 … (ii)
Multiply (i) by 3 and (ii) by 2: 72u + 108d = 18 and 72u + 48d = 13. Subtracting: 60d = 5 ⇒ d = 1/12, so downstream speed = 12 km/h.
Then 24u = 6 − 36/12 = 3 ⇒ u = 1/8, upstream speed = 8 km/h.
Stream speed = (12 − 8)/2 = 2 km/h (boat in still water = 10 km/h).
Check: 24/8 + 36/12 = 3 + 3 = 6 ✓; 36/8 + 24/12 = 4.5 + 2 = 6.5 ✓.
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