A boat running upstream takes 10 hours to cover a certain distance, while it takes 6 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

Question: A boat running upstream takes 10 hours to cover a certain distance, while it takes 6 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

Solution:
Let,
the man's rate upstream = x kmph
and that downstream = y kmph.

Then,
distance covered upstream in 10 hours = Distance covered downstream in 6 hours.
x × 10 = y × 6
⇒ 10x = 6y
⇒ 6y = 10x
⇒ y = 10x/6
∴ y = 5x/3

∴ Required ratio = {(y + x)/2} : {(y - x)/2}
= (y + x) : (y - x)
= (5x/3 + x) : (5x/3 - x)
= 8x/3 : 2x/3
= 8x : 2x
= 4 : 1