SOLUTION: Two cars start moving simultaneously in the same direction. The first car moves at 64 mph; the speed of the second car is 40 mph. A half-hour later, another car starts moving in th

Question 1089570: Two cars start moving simultaneously in the same direction. The first car moves at 64 mph; the speed of the second car is 40 mph. A half-hour later, another car starts moving in the same direction. The third car reaches the first one 1.5 hours after it reached the second car.
Find the speed of the third car.
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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Two cars start moving simultaneously in the same direction. The first car moves at 64 mph; the speed of the second car is 40 mph.
A half-hour later, another car starts moving in the same direction. The third car reaches the first one 1.5 hours after it reached the second car.
~~~~~~~~~~~~~~~~~~~~~

Let x be the speed of the third car in mph, which is under the question.

The third car reaches the second one in  hours.

The third car reaches the first one in  hours.

The condition says that 

 -  = 1.5   hour.


Simplify and solve for x.


You first step is to multiply both sides of the equation by (x-64)*(x-40).


I solved it mentally and got the answer x= 80 mph.

For many other solved catching up problems/samples see the lesson
- Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the section "Word problems", the topic "Travel and Distance problems".

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