Question:medium

A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

Updated On: Jan 15, 2026
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The Correct Option is A

Solution and Explanation

Two vehicles initiate movement from distinct locations towards each other. Vehicle 1 maintains a constant velocity of 60 km/hr, while Vehicle 2's velocity is undetermined. They converge after an interval of \( t \) hours. Based on the durations each vehicle requires to traverse the distance covered by the other, ascertain the velocity of Vehicle 2.

Definitions:

  • Velocity of Vehicle 2 = \( x \) km/hr
  • Time elapsed until convergence = \( t \) hours

Stage 1: Distance Covered

Over \( t \) hours:

  • Distance covered by Vehicle 1 = \( 60 \cdot t \) km
  • Distance covered by Vehicle 2 = \( x \cdot t \) km

Stage 2: Time for Vehicle 1 to Cover Vehicle 2's Distance

Information provided: Vehicle 1 traverses \( x \cdot t \) km in 45 minutes, equivalent to \( \frac{3}{4} \) hours.
\[ \frac{x \cdot t}{60} = \frac{3}{4} \] \[ \Rightarrow t = \frac{180}{4x} \tag{1} \]

Stage 3: Time for Vehicle 2 to Cover Vehicle 1's Distance

Information provided: Vehicle 2 traverses \( 60 \cdot t \) km in 20 minutes, equivalent to \( \frac{1}{3} \) hours.
\[ \frac{60 \cdot t}{x} = \frac{1}{3} \] \[ \Rightarrow t = \frac{x}{180} \tag{2} \]

Stage 4: Equating Expressions for \( t \)

\[ \frac{180}{4x} = \frac{x}{180} \] \[ \Rightarrow 4x^2 = 180 \cdot 180 = 32400 \] \[ \Rightarrow x^2 = \frac{32400}{4} = 8100 \] \[ \Rightarrow x = \sqrt{8100} = 90 \]

Conclusion: \( \boxed{90 \text{ km/hr}} \)

Corresponding Option: (A)

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