The Speed of a boat in still water is 15 km/h . It can go 30 km upstream and return to the original point in 4 hours 30 minutes. Find the speed of the stream.

Problem : The Speed of a boat in still water is 15 km/h . It can go 30 km upstream and return to the original point in 4 hours 30 minutes. Find the speed of the stream.

Doubt by Muskan

Solution :

Let the speed of the stream = x km/h
Speed of the boat = 15 km/h (Given)
Distance covered = 30 km (Given)

Total Speed of Boat during upstream = (15-x) km/h
Total speed of Boat during downstream = (15+x) km/h

We know, Speed = Distance / Time
Time = Distance / Speed

Time taken to cover 30 Km during upstream
t1 = 30/(15-x) hrs ---(1)

Time taken to cover 30 Km during downstream
t2 = 30/(15+x) hrs ---(2)

ATQ

t1 + t2 = 4 hrs + 30 minutes
30/(15-x) + 30/(15+x) = 4 + (30/60)30
[ 1/(15-x) + 1/((15+x)] = 4 + (1/2)30 
[ 1/(15-x) + 1/((15+x)] = 9/2
1/(15-x) + 1/ (15+x) = 9/(2x30) = 3/20
(15+x + 15 -x) / (15-x)(15+x) = 3/20
30 / (225 - x²) = 3/20
3 (225-x²) = 30 x 20
675 - 3x² = 600
675-600 = 3x²
75 = 3x²
x² = 75/3
x² = 25
x = ±√25
x = ± 5
x = + 5 or  x = -5
But x ≠ - 5 (Speed can't be negative)
Rejected.

Hence, x = 5

∴ Speed of the stream is 5 km/h