SOLUTION: when chris drives his car to work it takes 1/2 hour. when he takes the bus it takes 3/4 hour. the average rate of the bus is 12 mph less than his rate when driving. find the ditanc

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Question 838544: when chris drives his car to work it takes 1/2 hour. when he takes the bus it takes 3/4 hour. the average rate of the bus is 12 mph less than his rate when driving. find the ditance he travels to work.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Assign variables to whatever you not know.
Use RT=D and fill in a data table.

__________________speed___________time_________distance
CAR_________________r_____________1/2__________r(1/2)
BUS_______________(r-12)__________3/4_________(r-12)(3/4)

The car and the bus method use the same distance to reach the same destination, highlight_green%28r%281%2F2%29=%28r-12%29%283%2F4%29%29.
Solve for the rate first, and then you can compute the distance. Start the equation solving by multiplying both sides by 4:

2r=%28r-12%29%2A3
2r=3r-36
highlight%2836=r%29
-
Since the distance is r%281%2F2%29, this is highlight%2836%281%2F2%29=highlight%2818%29%29 miles