Question

The speed of a boat in still water is 11 km/h. It can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.

(a) 3 km/h
(b) 4 km/h
(c) 5 km/h
(d) 6 km/h

Answer 1

To find the speed of the stream, set up a system of equations based on the given information and solve for 's'.

Step-by-step explanation:

To find the speed of the stream, we can set up a system of equations based on the given information. Let's assume that the speed of the stream is 's' km/h.

When the boat goes upstream, its effective speed is the speed of the boat in still water minus the speed of the stream. So, the time taken to go upstream is equal to the distance divided by the effective speed:
12 km / (11 km/h - s km/h) = tupstream

When the boat goes downstream, its effective speed is the speed of the boat in still water plus the speed of the stream. So, the time taken to go downstream is equal to the distance divided by the effective speed:
12 km / (11 km/h + s km/h) = tdownstream

We are given that the total time taken for the round trip is 2 hours and 45 minutes, which is equal to 2.75 hours. We can set up the equation:
tupstream + tdownstream = 2.75

Solving these equations simultaneously will give us the speed of the stream, 's'.