SOLUTION: Two cars, A and B, 148 kilometers apart, traveled toward each other. A started at 6 a.m. while B started an hour later. They met on the road at 9 a.m. Had both of them started at 6

Question 1111099: Two cars, A and B, 148 kilometers apart, traveled toward each other. A started at 6 a.m. while B started an hour later. They met on the road at 9 a.m. Had both of them started at 6 a.m., they would have met at 8:28. Find the speed.
Answer by ikleyn(52833) (Show Source): You can put this solution on YOUR website!
.

1.  In the first scenario, 1-st car was on the way 3 hours (from 6 am till 9 am) before meeting.

                           2-nd car was on the way 2 hours before meeting.


    Let "a" and "b" be their rates in miles per MINUTE, respectively. 

    Then from the first scenario, the total distance between the cities was

        180a + 120b  = 148  miles.               (1)    (3 hours = 180 minutes;  2 hours = 120 minutes !)



2.  In the second scenario, each car was on the way 2 hours and 28 minutes = 148 minutes.  


    Therefore, the second equation for the entire distance is

        148a + 148b = 148  miles,   or

           a + b = 1       (miles per minute)     (2) 



3.  Thus you have this system of two equations in two unknowns

       a +    b =   1,    and

    180a + 120b = 148.


    Solve it by ANY method you want.  Both methods - Substitution and Elimination - are good.  Choose any and complete the solution on your own.



4.   H a p p y   s o l v i n g  ! !

RELATED QUESTIONS
Two travelers, A and B, 165 kilometers apart, traveled toward each other. A started at... (answered by richwmiller)

1. A crew rowed 7 miles upstream in 2 hours and the 6 1/2 miles downstream in 1 hour.... (answered by ikleyn)

Two vehicles 2000 m apart are approaching each other. Vehicle A is moving at a constant... (answered by ikleyn)

Two trucks started toward each other at the same time from towns 500 km apart. One truck... (answered by checkley77)

two cars, 380 kilometers apart, begin driving toward each other on a long, straight... (answered by richwmiller)

Ian and Carolyn are 200 feet apart when they begin walking directly toward one another.... (answered by ankor@dixie-net.com)

two cars will run for 10 kilometers,car A started 7 1/2 kilometers ahead, car B started... (answered by ankor@dixie-net.com)

Two trucks started toward each other at the same time from towns 500 km apart. One truck... (answered by josmiceli)

Two cars started from the same point and traveled on a straight course in opposite... (answered by checkley77)