At his usual rowing speed, Kapil can travel 12 miles downstream in a certain river in 6 h less than he takes to travel the same distance upstream. But, If he could double his usual rowing speed for his 24 miles round trip, the downstream 12 miles would then take only 1 h less than the upstream 12 miles. What is the speed of the current?

Let speed of Kapil in still water = x
and speed of the current= y
∴ Speed upstream = (x - y)
and speed downstream = (x + y)
According to the question,
12/(x - y) - 12/(x + y) = 6
⇒ 6(x² - y²) = 24y
⇒ x² - y² = 4y
⇒ x² = 4y + y² ....(i)
Again, 12/(2x - y) - 12/(2x + y) = 1
⇒ 4x² - y² = 24y
⇒ x² = (24y + y²)/4 ....(ii)
From Eqs. (i) and (ii), we get
4y + y² = (24y + y²)/4
⇒ 16y +4y² = 24y + y²
⇒ 3y² = 8y
∴ y = 8/3 = 2²/₃ mile/h