Two Buses: How Long to Catch Up?

  • Thread starter Jimbo57
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In summary, the time it takes for one bus to catch up to another can be calculated using the formula t = d / (v1 - v2), where t is the time, d is the distance between the two buses, v1 is the speed of the first bus, and v2 is the speed of the second bus. Two buses traveling in opposite directions can catch up to each other if one bus is traveling faster than the other or if they have different starting points. If one bus is traveling at a constant speed and the other bus is accelerating, it is still possible for the two buses to catch up to each other, but the time it takes will depend on the acceleration rate of the second bus. The distance between the two
  • #1
Jimbo57
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Homework Statement


Two buses are moving at constant speeds, in the same direction, the first at 42km/h and the second at 54km/h. They are 18km apart. How long will it take the second bus to catch up to the first?


Homework Equations





The Attempt at a Solution



Seems pretty easy, but I've been out of high school for a while so my confidence is relatively low. Here's my attempt:

42t = 54t - 18
18 = 54t - 42t
18 = 12t
t = 1.5 hours
 
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yep

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FAQ: Two Buses: How Long to Catch Up?

How do you calculate the time it takes for one bus to catch up to another?

The time it takes for one bus to catch up to another can be calculated using the formula t = d / (v1 - v2), where t is the time, d is the distance between the two buses, v1 is the speed of the first bus, and v2 is the speed of the second bus.

Can two buses ever catch up to each other if they are traveling in opposite directions?

Yes, two buses traveling in opposite directions can catch up to each other. This can happen if one bus is traveling faster than the other or if they have different starting points.

What happens if one bus is traveling at a constant speed and the other bus is accelerating?

If one bus is traveling at a constant speed and the other bus is accelerating, it is still possible for the two buses to catch up to each other. However, the time it takes for them to catch up will depend on the acceleration rate of the second bus.

Is the distance between the two buses always decreasing when one bus is trying to catch up to the other?

No, the distance between the two buses may not always be decreasing when one bus is trying to catch up to the other. This can happen if the second bus is traveling at a higher speed than the first bus or if the first bus is decelerating.

Are there any real-world applications of the "Two Buses" problem?

Yes, the "Two Buses" problem can be applied to real-world scenarios such as calculating the time it takes for a slower runner to catch up to a faster runner, or the time it takes for a car to catch up to a truck on the highway.

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