Two Buses: How Long to Catch Up?

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SUMMARY

The problem involves two buses traveling in the same direction, with the first bus moving at 42 km/h and the second at 54 km/h, starting 18 km apart. The equation derived from their speeds is 42t = 54t - 18. Solving this gives t = 1.5 hours, indicating that the second bus will catch up to the first in 1.5 hours.

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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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