A motorboat whose speed is 15 km/hr in still water goes 30km downstream and…
2025
A motorboat whose speed is 15 km/hr in still water goes 30km downstream and comes back in four and a half hours. The speed of the stream is:
- A.
3 km/hr
- B.
2 km/hr
- C.
4 km/hr
- D.
5 km/hr
Attempted by 15 students.
Show answer & explanation
Correct answer: D
Let x be the speed of the stream in km/hr.
Downstream speed = 15 + x km/hr. Upstream speed = 15 - x km/hr.
Total time for 30 km downstream and 30 km upstream is
30/(15 + x) + 30/(15 - x) = 4.5
Combine the fractions: 30[(15 - x) + (15 + x)]/(15 + x)(15 - x) = 4.5
Numerator simplifies to 30·30 = 900 and denominator to 225 - x^2, so 900/(225 - x^2) = 4.5
Multiply both sides: 900 = 4.5(225 - x^2). Multiply both sides by 2 to clear the decimal: 1800 = 9(225 - x^2)
Compute: 1800 = 2025 - 9x^2 ⇒ 9x^2 = 2025 - 1800 = 225 ⇒ x^2 = 25 ⇒ x = 5 (positive speed).
Check: downstream speed = 15 + 5 = 20 km/hr ⇒ time = 30/20 = 1.5 hr; upstream speed = 15 - 5 = 10 km/hr ⇒ time = 30/10 = 3 hr; total = 4.5 hr.
Answer: The speed of the stream is 5 km/hr.