A man takes 20 minutes to row 12 km upstream which is one-third more than the time he takes on his way downstream. What is his speed in still water?

Question: A man takes 20 minutes to row 12 km upstream which is one-third more than the time he takes on his way downstream. What is his speed in still water?

Solution:
Let,
His speed in still water is x km/hr
The speed of stream is y km/hr
Time taken downstream is t min
ATQ,
t + (t/3) = 20 min
⇒ (3t + t)/3 = 20
⇒ 4t = 20 × 3
⇒ t = 60/4
∴ t = 15 min

In 20 minutes he rows in upstream 12 km
∴ In 60 minutes he rows in upstream (12 × 60)/20 km
= 36 km

∴ x - y = 36 ..............(1)


In 15 minutes he rows In downstream 12 km
∴ In 60 minutes he rows In downstream (12 × 60)/15 km
= (720 × 3)/40 km
= 48 km

∴ x + y = 48 ................(2)

From (2) + (1) we get,
x + y + x - y = 48 + 36
⇒ 2x = 84
∴ x = 42

∴ His speed in still water is 42 km/hr