what’s the rate of the slower bus and the faster bus?

Question

Two buses leave a station at the same time and travel in opposite directions. One bus travels 12 km/h slower than the other. If the two buses are 920 km apart after 4 hours, what is the rate of each bus?

Answer 1

Fast bus has speed v, slow bus has speed v - 12.  Travel time for both is t = 4.

 

vt + (v - 12)t = 920 km

 

t =  4 hrs

 

4v + 4(v - 12) = 920

v + v - 12 = 230

 

2v = 230 + 12 = 242

 

v = 242/2 = 121 km/hr  [speed of fast bus]

v - 12 = (121 - 12) km/hr = 109 km/hr  [speed of slow bus]

 

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