Two Buses: How Long to Catch Up?

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Two buses are traveling in the same direction, with speeds of 42 km/h and 54 km/h, and they are initially 18 km apart. To determine how long it will take for the second bus to catch up to the first, the equation 42t = 54t - 18 is used. Simplifying this leads to 18 = 12t, resulting in t = 1.5 hours. The solution indicates that the second bus will catch up to the first in 1.5 hours. This problem highlights the application of relative speed in motion scenarios.
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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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