Question

the speed of the boat in still water in 8 kilometre per hour it can go 15 kilometre upstream and 22 kilometre downstream in 5 hours find the speed of the stream​

Answer 1

Given

★ Speed of the boat in still water = 8 km/h

★ Distance travelled (upstream) = 15 km

★ Distance travelled (downstream) = 22 km

★ Total time taken = 5 h

To find

★ Speed of the stream

Solution

let the speed of the stream = x km/h

★ Case 1 (upstream)

Net speed of the boat = (8 - x) km/h

★ Case 2 (downstream)

Net speed of the boat = (8 + x) km/h

We know that

Time = Distance/ Speed

It is given that the boat takes 5 hours to travel upstream and downstream simultaneously

Time (upstream) + Time (downstream) = Total time

▶ 15/(8 - x) + 15/(8 + x) = 5

▶ {15(8 + x) + 22(8 - x)} / {64 - x²} = 5

On cross multiplying

▶ 120 + 15x + 176 - 22x = 320 - 5x²

▶ 296 - 7x = 320 - 5x²

▶ 5x² - 7x - 24 = 0

▶ 5x² - 15x + 8x - 24 = 0

▶ 5x (x - 3) + 8 (x - 3) = 0

▶ (5x + 8) (x - 3) = 0

▶ x = -8/5 or 3

Since, speed cannot be negative

∴ The speed of the stream = 3 km/h

Answer 2

See in attachment..

Hope its helpful ❤️