Car chase: 45 km behind, 90 and 75 km/h

A car starts 45 km behind another car, and both drive in the same direction at 90 km/h and 75 km/h. After how many hours does the faster car catch up?

Step-by-step

1. 90 − 75 = 15
   Moving the same way, the relative speed is the difference of the speeds
2. 45 ÷ 15 = 3
   Catch-up time = distance ÷ relative speed

Why it works

The faster car gains on the slower one at the difference of their speeds, so the time to close a 45 km gap is the gap divided by that difference.

Common mistakes

• Adding the speeds instead of subtracting them.
• Dividing 45 km by 90 km/h.

Related

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