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CAT 2022 Slot 2 — QA Question 21

Relative SpeedEasy

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

Answer & solution

  • 18

  • B

    24

  • C

    12

  • D

    20

Solution

Easy

South and west are perpendicular, so the two ships' paths form the legs of a right triangle with the 6060 km gap as hypotenuse. Apply Pythagoras to the distances covered in 2 hours.

meet 2x 2(x+6) 60
1

Distances in 2 hours. Slower ship speed xx; faster x+6x+6:

legs=2x and 2(x+6),hypotenuse=60\text{legs}=2x\ \text{and}\ 2(x+6),\quad \text{hypotenuse}=60
2

Pythagoras:

(2x)2+(2(x+6))2=6024x2+4(x2+12x+36)=36008x2+48x+144=3600\begin{aligned} &(2x)^2+\big(2(x+6)\big)^2=60^2\\ &4x^2+4(x^2+12x+36)=3600\\ &8x^2+48x+144=3600 \end{aligned}
3

Simplify and factor (divide by 8):

x2+6x−432=0(x−18)(x+24)=0 ⇒ x=18(x>0)\begin{aligned} &x^2+6x-432=0\\ &(x-18)(x+24)=0\ \Rightarrow\ x=18\quad(x>0) \end{aligned}
Speed of slower ship=18 km/h\text{Speed of slower ship}=\mathbf{18}\text{ km/h}
CAT 2022 Slot 2 QA Q21: Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at const — Solution | TheCATExam