CAT 2022 Slot 2 QA Question 21: Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 k

Question

Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 k

Accepted Answer

Let the speed of the slower ship be $v$ km/hr. Then the speed of the faster ship is $v + 6$ km/hr.

In 2 hours, the two ships travel $2v$ and $2(v + 6)$ km in perpendicular directions.

Using Pythagoras theorem:

$(2v)^2 + (2(v + 6))^2 = 60^2$
$4v^2 + 4(v + 6)^2 = 3600$
$v^2 + (v + 6)^2 = 900$
$2v^2

Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is