The difference between the time taken by 2 cars to cover 450 Km is 1 hour 30 minutes. If the difference between their speeds is 15 Kmph, find the speed of the slower car?

Solution

Let the speed of the slower car be \(v\) km/h, and the speed of the faster car be \(v + 15\) km/h.

Given:
– The difference in time taken by the two cars to cover 450 km is 1 hour 30 minutes (which is 1.5 hours).
– The difference in their speeds is 15 km/h.

Step 1: Express the time taken by each car to cover 450 km

– Time taken by the slower car: \(\frac{450}{v}\) hours
– Time taken by the faster car: \(\frac{450}{v + 15}\) hours

Step 2: Set up the equation based on the difference in time taken

\[ \frac{450}{v} – \frac{450}{v + 15} = 1.5 \]

Step 3: Solve the equation

Multiplying all terms by \(v(v + 15)\) to clear the denominators:
\[ 450(v + 15) – 450v = 1.5v(v + 15) \]
\[ 450v + 6750 – 450v = 1.5v^2 + 22.5v \]
\[ 6750 = 1.5v^2 + 22.5v \]
\[ v^2 + 15v – 4500 = 0 \]

Factoring the quadratic equation:
\[ (v + 75)(v – 60) = 0 \]

Since the speed cannot be negative, we take the positive value:
\[ v = 60 \]

Conclusion

The speed of the slower car is 60 km/h.