A truck left the station at 6 a. m. traveling at a rate of 45 km/h. A van left the same place 2 hours later heading in the same direction at a rate of 54 km/h. At what time will the van catch up with the truck?

Question

Mathematics

Imani Chen

17 July, 02:09

A truck left the station at 6 a. m. traveling at a rate of 45 km/h. A van left the same place 2 hours later heading in the same direction at a rate of 54 km/h. At what time will the van catch up with the truck?

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Answers (1)

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Darion Becker · Answer 1

6 PM

Step-by-step explanation:

The truck has a 2 hour head start. It is moving at 45 km/h, so it is 90 km ahead.

If t is the time after 8 AM, then the distance between the truck and the station is:

d = 90 + 45t

The distance between the van and the station is:

d = 54t

When the distances are equal:

54t = 90 + 45t

9t = 90

t = 10

It takes 10 hours after 8 AM for the van to catch up with the truck. So the time would be 6 PM.