Boats and Stream

Objectives

This Chapter introduces you to the concepts of how to solve questions of Boats and Stream with complete ease.

Qu. 01: A boat runs at 22 km per hour along the stream and 10 km per hour against the stream. Find the ratio of speed of the boat in still water to that of the speed of the stream.

Sol: Let the speed of boat in still water be P km/h.

Let the speed of stream be Q km/h.

Given, P + Q = 22 and P – Q = 10. These two equations give:

P = 16, Q = 6. Hence, P: Q = 16: 6 = 8: 3. Ans.

Qu. 02: A boat travels upstream from B to A and downstream from A to B in 3 h. If the speed of the boat in still water is 9 km/h and the speed of the current is 3 km/h, what distance between A and B?

Sol: If T is the time taken in upstream motion and t is the time taken in downstream motion, given, T + t = 3

Since, distance = speed x time, we have for upstream motion, d = (9 – 3) x T, and, for downstream motion, d = (9 + 3) x t. These give:

d = 6T and, d = 12t; or, 6T = 12t; or, T = 2t.

Since, T + t = 3, we have, t = 1, T = 2.

Hence, d = 6T = 12 km. Ans.

Qu. 03: What is the speed of the current, if a boat covers 120 km downstream and 40 km upstream in it in 4 hours?

Sol: Let the speed of boat in still water be P km/h.

Let the speed of current be Q km/h.

Since, speed = distance / time, and both journeys (upstream and downstream) take 4 hours each, we have:

P + Q = 120/4 = 30, and, P – Q = 40/4 = 10. These give: P = 20 and Q = 10.

The speed of current is 10 km/h. Ans.