Question

the speed of a boat in still water is 15 km / hr . it can go 30 km upstream and return downstream to the orginal point in 4 hours and 30 minutes . find the speed of the stream .

Answer 1

Let speed of stream = x km/h
∴ Downstream speed = (15+x) km/h
∴ Upstream speed = (15-x) km/h
∴ 30/(15+x) + 30/(15-x) = 4 1/2
→ 900/225-x² = 9/2
→ 9x² = 225
→ x² = 25
→ x = 5
∴ Speed of stream = 5 km/h

Answer 2

Solution :-

Let the speed of the train be x km/h.

Downstream speed = (15 + x) km/h

Upstream speed = (15 - x) km/h

Time taken to go 30 km upstream = 30/(15 - x) hrs.

Time taken to go 30 km downstream = 30/(15 + x) hrs.

According to the Question,

⇒ 30/(15 - x) + 30/(15 + x) = 9/2

⇒ 30(15 + x) + 30(15 - x)/(15 + x) (15 - x) = 9/2

⇒ 450 + 30x + 450 - 30x/225 - x² = 9/2

⇒ 900/225 - x² = 9/2

By cross-multiplication, we get

⇒ 9(225 - x²) = 1800

⇒ 225 - x² = 200

⇒ x² = 25

⇒ x = ± 5

(As speed can't be negative)

⇒ x = 5 km/h

Hence, the speed of stream is 5 km/h.