Question

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

• A. 150
• B. 100
• C. 90
• D. 120

Answer 1

The Correct Option is C

The correct answer is C:90
Let's denote the speed of the faster car as "v"km/hr.We're given that the speed of the slower car is 60km/hr.
When the two cars travel towards each other, their effective speed is the sum of their speeds:
Effective speed=Speed of slower car+Speed of faster car=60+v km/hr
When the two cars travel in the same direction,the effective speed is the difference of their speeds:
Effective speed=Speed of faster car-Speed of slower car=v-60 km/hr
We are given the time it takes for them to meet in both scenarios:
1.5 hours when traveling towards each other,and 10.5 hours when traveling in the same direction.
Let's set up the equations based on the time,speed, and distance relationship:
When traveling towards each other:
\(Distance=Speed\times{Time}\)
\(Distance = (60 + v)\times1.5 km\)
When traveling in the same direction:
\(Distance = Speed \times Time\)
\(Distance = (v - 60)\times10.5 km\)
Since the distances in both scenarios are the same (since they meet at the same point):
\((60+v)\times1.5=(v-60)\times10.5\)
Now we can solve for "v":
90+1.5v=10.5v-630
9v=720
v=80
So,the speed of the faster car is 80km/hr.
Now that we know the speed of the slower car is 60km/hr and the speed of the faster car is 80km/hr,we can calculate the distance traveled by the slower car when they meet while traveling towards each other:
\(Distance = Speed\times{Time}\)\(Distance = 60 \times 1.5 = 90 km\)
Therefore,the slower car travels 90km when it meets the other car while traveling towards each other.

Answer 2

When car travel towards each other, then both cars take 1.5 hrs to meet.
The speed of slower car \(= 60\) km/hr
Hence, distance covered by the slower car before they meet,
\(= 60\times1.5\)
\(= 90\ km\)

So, the correct option is (C): \(90\)