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
- 90
- 100
- 80
- 70
The Correct Option is A
Solution and Explanation
Two cars start from different points and move towards each other. Car 1 travels at 60 km/hr and Car 2 travels at an unknown speed. They meet after \( t \) hours. Given the travel durations for each car's leg of the other's distance, find the speed of Car 2.
Let:
- Speed of Car 2 = \( x \) km/hr
- Time taken by both cars to meet = \( t \) hours
Step 1: Distances traveled
In \( t \) hours:
- Car 1 travels = \( 60 \cdot t \) km
- Car 2 travels = \( x \cdot t \) km
Step 2: Time taken by Car 1 to travel Car 2's distance
Given: Car 1 takes 45 minutes = \( \frac{3}{4} \) hours to cover \( x \cdot t \) km.
\[ \frac{x \cdot t}{60} = \frac{3}{4} \] \[ \Rightarrow t = \frac{180}{4x} \tag{1} \]
Step 3: Time taken by Car 2 to travel Car 1's distance
Given: Car 2 takes 20 minutes = \( \frac{1}{3} \) hours to cover \( 60 \cdot t \) km.
\[ \frac{60 \cdot t}{x} = \frac{1}{3} \] \[ \Rightarrow t = \frac{x}{180} \tag{2} \]
Step 4: Equating both expressions for \( t \)
\[ \frac{180}{4x} = \frac{x}{180} \] \[ \Rightarrow 4x^2 = 180 \cdot 180 = 32400 \] \[ \Rightarrow x^2 = \frac{32400}{4} = 8100 \] \[ \Rightarrow x = \sqrt{8100} = 90 \]
Final Answer: \( \boxed{90 \text{ km/hr}} \)
Correct Option: (A)
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