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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?

Respuesta :

MathPhys

Answer:

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.

The time in which the van catch up with the truck is 6 PM.

Given that,

  • 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.

Based on the above information, the calculation is as follows:

  • Since the truck has 2 hour head start that moves at 45 km/h so it should be 90 km ahead.
  • T be the time after 8 AM so the distance should be d = 90 + 45t  and d = 54t

Now  

54t = 90 + 45t

9t = 90

t = 10

The time that takes 10 hours after 8 AM that should be 6 PM.

Learn more: brainly.com/question/17429689

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