CAT 2023 Slot 3 QA Question 13: A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If

Question

A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If

Accepted Answer

Let the distance AB be d. For the first boat, downstream and upstream speeds are

$u + r = \dfrac{d}{2}$
$u - r = \dfrac{d}{3}$

Solving these gives the river speed:

$2r = \dfrac{d}{2} - \dfrac{d}{3} = \dfrac{d}{6}$
$r = \dfrac{d}{12}$

Let the still-water speed of the second boat be v. Its total u