Question 214139
Two buses leave the same city at the same time moving in opposite directions. One travels at a rate of 5 miles per hour faster then the other bus. After 3 hours they are 375 miles apart. How far did each bus travel.


Step 1.  Let x be the speed of one bus and let x+5 be the speed of the other bus.


Step 2.  Distance = speed * time


Step 3.  Distance of one bus = 3x and Distance of other bus = 3(x+5).


Step 4.  Total Distance = Distance of one bus + Distance of other bus = 375 miles


Step 5.  Combine steps 2 and 3 to get  3x+3(x+5)=375 or 6x+15=375.  Solving for x yields the following steps.


*[invoke explain_simplification "6x+15=375" ]


Step 6.  Based on the above results when x=60, then distance traveled by one bus is 3x=180  miles and the other bus traveled 3(x+5)=195  miles.   Adding the two distances yield that they are 375 miles part.


Step 7.  ANSWER:  One bus traveled 180 miles and the other traveled 195 miles.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J