Two places A and B are 70 km apart. A car starts from A and another car starts from B at the same time. If they move in the same direction they meet in 7 hours and if they move towards each other, they meet in \(2\frac{1}{3}\) hours. What are the speeds of the cars?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 20 km/h, 10 km/h
The gap of 70 km closes at the difference of the speeds when the cars move in the same direction, and at the sum of the speeds when they move towards each other. Let the speeds be \(u\) and \(v\) km/h, with \(u\gt v\).
Same direction: \(\displaystyle u-v=\frac{70}{7}=10\) (1)
Towards each other: \(\displaystyle u+v=\frac{70}{7/3}=30\) (2)
Adding (1) and (2), \(v\) cancels: \(2u=40\), so \(u=20\)
From (2): \(v=30-20=10\)