The speed of a boat in still water is 18 km/hr . it takes twice as long to go…
2023
The speed of a boat in still water is 18 km/hr . it takes twice as long to go upstream to a point as to return downstream to the starting point . What is the speed of the current ?
- A.
4 km/hr
- B.
10 km/hr
- C.
8 km/hr
- D.
6 km/hr
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Let the speed of the current be x km/hr.
Boat speed in still water = 18 km/hr, so downstream speed = 18 + x km/hr and upstream speed = 18 - x km/hr.
Let the distance to the point be d km. Then time upstream = d/(18 - x) and time downstream = d/(18 + x). The problem states the upstream time is twice the downstream time:
d/(18 - x) = 2 × d/(18 + x).
Cancel d (d > 0): 1/(18 - x) = 2/(18 + x). Cross-multiply and solve:
18 + x = 2(18 - x)
18 + x = 36 - 2x ⇒ 3x = 18
x = 6 km/hr
Answer: 6 km/hr.