A motor boat, whose speed is 20 km/hr in still water takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.

Let, the speed of the stream be x km/hr
Speed of boat in still water = 20 km/hr
∴Speed of boat with downstream 20+x km/hr
∴Speed of boat with upstream 20−x km/hr
As per given condition
48/(20−x) + x = 1
⇒48[(20+x) + (20−x)]/(20−x)(20+x) = 1
⇒48/(400−x²) = 1
48 = 400−x²
⇒x² + 48 = 400
⇒x² = 400 − 48
⇒x² = 352
⇒x = √352
⇒x ≈ 18.76 km/hr
Time taken to go upstream = 48/(20-x)
Time taken to go downstream = 48/(20+x)
Given that time taken to go upstream is 1 hour more than time taken to go downstream
48/(20-x) = 48/(20+x) + 1
48(20+x) = 48(20-x) + (20-x)(20+x)
960 + 48x = 960 - 48x + 400 - x²
96x + x² = 400
x² + 96x - 400 = 0
Solving the quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
x = (-96 ± √(96² - 4 * 1 * -400))/2
x = (-96 ± √(9216 + 1600))/2
x = (-96 ± √10816)/2
x = (-96 ± 104)/2
x = 4 or x = -100
Since speed cannot be negative, x = 4 km/hr
Therefore, the speed of the stream = 4 km/hr