Relative Speed and Distance Traveled

CAT 2022 Slot 3 · QA · Medium · Arithmetic

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Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

  1. A.

    150

  2. B.

    100

  3. C.

    90

  4. D.

    120

Answer

C

Explanation

Let the speeds of the two cars be v1v_1 and v2v_2 with v1>v2=60 km/hrv_1 > v_2 = 60\text{ km/hr}. Let the distance between their starting locations be DD.

When traveling towards each other: Dv1+60=1.5  ⟹  D=1.5(v1+60)\frac{D}{v_1 + 60} = 1.5 \implies D = 1.5(v_1 + 60)

When traveling in the same direction: Dv1−60=10.5  ⟹  D=10.5(v1−60)\frac{D}{v_1 - 60} = 10.5 \implies D = 10.5(v_1 - 60)

Equating expressions for DD: 1.5(v1+60)=10.5(v1−60)1.5(v_1 + 60) = 10.5(v_1 - 60) v1+60=7(v1−60)=7v1−420v_1 + 60 = 7(v_1 - 60) = 7v_1 - 420 6v1=480  ⟹  v1=80 km/hr6v_1 = 480 \implies v_1 = 80\text{ km/hr}

When traveling towards each other, they take 1.5 hours to meet. Distance traveled by the slower car =60×1.5=90 km= 60 \times 1.5 = 90\text{ km}.

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