Two cars on one road
✓ With solution
Two cars set off at the same moment from opposite ends of one road. We know how long each needed after they met… so when did they meet?
Salim drives from the village to the city. At the very same moment, Hala drives from the city to the village on the same road. Each drives at a steady speed that never changes, but their speeds are different. They pass each other and wave, then carry on: Salim needs 4 more hours to reach the city, and Hala needs just 1 more hour to reach the village.
How long after setting off did they meet?
- AAn hour and a half
- BTwo hours
- CTwo and a half hours
- DThree hours
Show the answer
Answer: B) Two hours. Call the meeting time t hours. The part of the road Hala covered before they met, in t hours, is exactly what Salim still had left, which took him 4 hours, so Hala is 4 ÷ t times as fast as Salim. The part Salim covered before they met, in t hours, took Hala just 1 hour afterwards, so Hala is t times as fast as him. Both describe the same thing, so 4 ÷ t = t, which means t × t = 4 and t = 2: they met after two hours, and Hala is twice as fast. Check: what Salim drove in two hours takes Hala one hour, and what Hala drove in two hours (twice as far) takes Salim 4 hours. The trap is two and a half hours, which is just the average of 4 and 1.
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