KA-0162Rate, time, distance
3 points, difficulty 1 of 3Level 9–10about 75sTwo towns are 300 km apart. A car leaves each town at the same moment driving toward the other, one at 60 km/h and the other at 90 km/h. How long until they meet?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
The gap closes from both ends at once.
2The strategy
Every hour the gap closes by 60 + 90 = 150 km.
3The full solution
300 / 150 = 2 hours.
Solution
The reliable way
When two objects move toward each other, the distance between them closes at the sum of their speeds. Here the gap shrinks by 60 + 90 = 150 km every hour, so a 300 km gap closes in 300 / 150 = 2 hours. Check it directly: in 2 hours the first car covers 120 km and the second covers 180 km, and 120 + 180 = 300. The transferable idea: approaching speeds add, receding speeds also add, and same-direction speeds subtract.
The elegant way
In two hours the cars cover 120 and 180 km, and those already fill the 300 km road.
Why this is on the test: Closing speed is the one idea that turns most two-object motion problems into a single division.