A motorboat whose speed is 20 km/hr in still water goes 40 km downstream and…
2023
A motorboat whose speed is 20 km/hr in still water goes 40 km downstream and comes back in a total of 5 hours. The speed of the stream (in km/hr) is:
- A.
9
- B.
6
- C.
12
- D.
10
Attempted by 12 students.
Show answer & explanation
Correct answer: A
Answer: 9 km/hr
Let the speed of the stream be x km/hr. Then:
Downstream speed = 20 + x km/hr; time for 40 km = 40/(20 + x) hours.
Upstream speed = 20 - x km/hr; time for 40 km = 40/(20 - x) hours.
Total time given: 40/(20 + x) + 40/(20 - x) = 5.
Solve the equation:
Multiply both sides by (20 + x)(20 - x) = 400 - x² to obtain: 40(20 − x) + 40(20 + x) = 5(400 − x²).
Left side simplifies to 1600, so 1600 = 2000 − 5x².
Rearrange: 5x² = 2000 − 1600 = 400, so x² = 80.
Therefore x = √80 = 4√5 ≈ 8.944 km/hr, which rounds to 9 km/hr.
Check: Using x ≈ 8.944, downstream time ≈ 40/(28.944) and upstream time ≈ 40/(11.056); their sum is 5 hours, confirming the result.
Thus the stream speed is 9 km/hr (approximately).