Finding Speeds of Two Cars

Video Explanation

Question

Places A and B are 100 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 5 hours. If they move towards each other, they meet in 1 hour. Find the speeds of the two 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: Form Equations

Same direction (difference of speeds):

\[ |x – y| = \frac{100}{5} = 20 \quad (1) \]

Opposite direction (sum of speeds):

\[ x + y = \frac{100}{1} = 100 \quad (2) \]

Step 4: Solve Linear Equations

Assume \(x > y\):

\[ x – y = 20 \]

\[ x + y = 100 \]

Add:

\[ 2x = 120 \Rightarrow x = 60 \]

Substitute:

\[ 60 + y = 100 \Rightarrow y = 40 \]

Conclusion

\[ \text{Speeds of cars} = 60 \text{ km/h and } 40 \text{ km/h} \]

Verification

Same direction: Relative speed = \(60 – 40 = 20\) → time = \(100/20 = 5\) ✔

Opposite direction: Relative speed = \(60 + 40 = 100\) → time = \(100/100 = 1\) ✔