Time, Speed and Distance Question 2 - CAT 2022
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:
Step-by-Step Explanation
Let the speed of the slower ship be x km/h. The speed of the faster ship is (x + 6) km/h.
In 2 hours, the distances covered by the ships along their perpendicular paths are:
Distance slower = 2x
Distance faster = 2(x + 6) = 2x + 12
Since one travels south and the other west, they form a right-angled triangle with a hypotenuse of 60 km:
(2x)² + (2x + 12)² = 60²
4x² + 4(x + 6)² = 3600
x² + (x² + 12x + 36) = 900
2x² + 12x − 864 = 0
x² + 6x − 432 = 0
(x + 24)(x − 18) = 0
Since speed must be positive, x = 18 km/h.
Correct Option: C
💡 FundaMakers Tip:
Avoid solving long quadratic equations by using Pythagorean Triplets. The hypotenuse is 60 km. Think of a standard right triangle scaled up to a hypotenuse of 60 (like the 3-4-5 triplet multiplied by 12, which gives 36-48-60).
This means the distances traveled in 2 hours must be 36 km and 48 km. Dividing these distances by 2 hours gives the speeds: 18 km/h and 24 km/h. The difference between them is exactly 6 km/h, which confirms 18 km/h is the correct answer in seconds.