Question:medium

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 60km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

Updated On: Jan 15, 2026

  • 150

  • 100

  • 90

  • 120

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The Correct Option is C

Solution and Explanation

Two vehicles, one with a higher velocity than the other, are in motion. They are either moving towards each other or in the same direction. The velocity of the slower vehicle is 60 km/h. The time until they meet is:

  • 1.5 hours when traveling in opposing directions.
  • 10.5 hours when traveling in the same direction.

Determine the distance covered by the slower vehicle in the scenario where they travel towards each other.

Step 1: Variable Definition

  • Let the velocity of the faster vehicle be \( v \) km/h.
  • Velocity of the slower vehicle = 60 km/h.

Step 2: Applying the Formula: Velocity × Time = Distance

Scenario 1: Traveling Towards Each Other

Combined velocity = \( v + 60 \) km/h.
Time elapsed = 1.5 hours.
\[ \text{Distance} = (v + 60) \times 1.5 \]

Scenario 2: Traveling in the Same Direction

Relative velocity = \( v - 60 \) km/h.
Time elapsed = 10.5 hours.
\[ \text{Distance} = (v - 60) \times 10.5 \]

Step 3: Equating Distances

The total distance covered in both scenarios is the same:

\[ (v + 60) \times 1.5 = (v - 60) \times 10.5 \]

Step 4: Solving for \( v \)

\[ 1.5v + 90 = 10.5v - 630 \]

\[ 90 + 630 = 10.5v - 1.5v \]

\[ 720 = 9v \]

\[ v = \frac{720}{9} = 80 \]

Therefore, the velocity of the faster vehicle is \( \boxed{80 \text{ km/h}} \).

Step 5: Calculating the Distance Traveled by the Slower Vehicle

Using the time from the first scenario (1.5 hours) and the velocity of the slower vehicle (60 km/h):

\[ \text{Distance} = 60 \times 1.5 = \boxed{90 \text{ km}} \]

Final Answer:

The distance covered by the slower vehicle in the first case is \( \boxed{90 \text{ km}} \). (Correct Option: C)

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