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

Two cars, one faster than the other, travel either towards each other or in the same direction. The slower car has a speed of 60 km/h. They meet after:

• 1.5 hours when traveling towards each other
• 10.5 hours when traveling in the same direction

What is the distance covered by the slower car in the first case?

Step 1: Define the Variables

• Let the speed of the faster car be \( v \) km/h
• Speed of the slower car = 60 km/h

Step 2: Use Time × Speed = Distance

Case 1: Traveling Towards Each Other

Effective speed = \( v + 60 \) km/h
Time = 1.5 hours
\[ \text{Distance} = (v + 60) \times 1.5 \]

Case 2: Traveling in Same Direction

Effective speed = \( v - 60 \) km/h
Time = 10.5 hours
\[ \text{Distance} = (v - 60) \times 10.5 \]

Step 3: Equating the Distances

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

Step 4: Solve for \( v \)

\[ 1.5v + 90 = 10.5v - 630 \Rightarrow 90 + 630 = 10.5v - 1.5v \Rightarrow 720 = 9v \Rightarrow v = 80 \]

So, the speed of the faster car is \( \boxed{80 \text{ km/h}} \)

Step 5: Calculate the Distance Traveled by Slower Car

Using the time in the first case (1.5 hours) and speed of the slower car (60 km/h): \[ \text{Distance} = 60 \times 1.5 = \boxed{90 \text{ km}} \]

Final Answer:

\[ \boxed{90 \text{ km}} \quad \text{(Correct Option: C)} \]

Answer 2

Two cars travel towards each other and meet after 1.5 hours. The speed of the slower car is 60 km/h. Find the distance traveled by the slower car before they meet.

Step-by-Step Solution:

• Speed of slower car = \( 60 \) km/h
• Time taken before meeting = \( 1.5 \) hours

Using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \]

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

Final Answer:

\[ \boxed{90} \]

Correct Option: (C)