Finding Speeds of Two Cars

Video Explanation

Question

Places A and B are 80 km apart. Two cars start at the same time, one from A and the other from B. If they move in the same direction, they meet in 8 hours. If they move in opposite directions, they meet in 1 hour 20 minutes. Find the speeds of the cars.

Solution

Step 1: Concept

Relative Speed = Distance / Time

Step 2: Let Variables

Let speed of first car = \(x\) km/h

Let speed of second car = \(y\) km/h

Step 3: Convert Time

1 hour 20 minutes = \( \frac{4}{3} \) hours

Step 4: Form Equations

Same direction (relative speed = difference):

\[ |x – y| = \frac{80}{8} = 10 \quad (1) \]

Opposite direction (relative speed = sum):

\[ x + y = \frac{80}{\frac{4}{3}} = 60 \quad (2) \]

Step 5: Solve Linear Equations

Assume \(x > y\):

\[ x – y = 10 \]

\[ x + y = 60 \]

Add:

\[ 2x = 70 \Rightarrow x = 35 \]

Substitute:

\[ 35 + y = 60 \Rightarrow y = 25 \]

Conclusion

\[ \text{Speeds of cars} = 35 \text{ km/h and } 25 \text{ km/h} \]

Verification

Same direction: Relative speed = \(35 – 25 = 10\) → time = \(80/10 = 8\) ✔

Opposite direction: Relative speed = \(35 + 25 = 60\) → time = \(80/60 = \frac{4}{3}\) ✔