A boat takes 19 hours for travelling downstream from point A to point B and…
2024
A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 km/h and the speed of the boat in still water is 14 km/h, what is the distance between A and B?
- A.
200 km
- B.
180 km
- C.
160 km
- D.
220 km
Attempted by 6 students.
Show answer & explanation
Correct answer: B
Solution:
Let the distance between A and B be x km.
Downstream speed = 14 + 4 = 18 km/h. Upstream speed = 14 - 4 = 10 km/h.
Time taken downstream (A to B) = x/18. Time taken upstream from B to midpoint C = (x/2)/10 = x/20.
Total time = x/18 + x/20 = 19 hours. Solve for x:
Combine the fractions: x/18 + x/20 = (10x + 9x)/180 = 19x/180.
Set 19x/180 = 19 ⇒ x = 19 * 180 / 19 = 180.
Therefore the distance between A and B is 180 km.