A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.

Average speed of boat = 3.67 km/h

Average speed of stream = 0.63 km/h

Step-by-step explanation:

30 km upstream in 10 hours gives a speed of 30/10 = 3 km/h relative speed of boat and stream

Same way, 44 km in 10 hrs = 4.4 km/h relative speed of boat and stream.

Let the speed of the stream be y

Let the speed of both be x, then

x - y = 3 ... (1)

x + y = 4.4 ... (2)

Subtract 1 from 2

2y = 1.4

y = 1.4/2 = 0.7 km/h

substitute value of y in 1

x - 0.7 = 3

x = 3.7 km/h

Also, 40 km upstream in 13 hrs gives speed of 3.08 km/h

55 km in 13 hrs gives 4.2 km/h

Let speed of boat be x and that of stream be y

x - y = 3.08 ... (1)

x + y = 4.2 ... (2)

Subtract 1 from 2

2y = 1. 12

y = 0.56 km/h

Substitute value of y in 1

x - 0.56 = 3.08

x = 3.64 km/h

Average speed of boat = (3.7 + 3.64) / 2

= 3.67 km/h.

Average speed of stream = (0.7 + 0.56) / 2 = 0.63 km/h