College Algebra: Find average speeds of car and bus

[daniel]

Joe and Sally have a fight and break up. Sally boarsd a bus at the bus terminal at 10am and leaves town. At noon the same day, Joe leaves from the same bus terminal in his car and travels the same route in order to catch up with the bus and beg Sally for forgiveness. Joe averages 24mph faster than the bus and he over takes the bus 288 miles from the terminal. Find the average speed of the bus and the average speed of the car. Use an equation and show all work.

This is what I got so far: x=speed of bus, x+24=speed of car
so bus is 288/x and car is 288/x+24
288 288
--- = ----- +2, Then i multiplied each part by x(x+24) and got 288(x+24)=288x+2x(x+24)
x x+24 Then after all that I got 0=2x^2+48x-6912,
but I don't know what to do from here. Can anyone please help?

 

[Loren]

..............rate......X....time = dist
Sally.........r........X.....t....= 288
Joe........r+24......X.....t-2..= 288

If you must use only one variable then let's see what you did....

This is what I got so far: x=speed of bus, x+24=speed of car
so bus is 288/x and car is 288/x+24 <<<Do a better job labeling--- "time bus is traveling = 288/x" and "time car is traveling = 288/(x+24)" <<< Note parenthesis.
288 288
--- = ----- +2, Then i multiplied each part by x(x+24) and got 288(x+24)=288x+2x(x+24)
x x+24
Then after all that I got 0=2x^2+48x-6912

GOOD!!! Divide both sides by 2. Find two numbers that multiply together to get -3456 and add together to get +24. One of them is about 46, 48 or 50.

 

[daniel]

ok thanks, but why do you divide everything by 2? thats the part I dont get...

 

[Loren]

The idea is that if something is equal to something else, then half of that something is equal to half of the something else. By dividing both sides of the equation by any non-zero integer except one, you will be working with smaller numbers. You don't have to dive this equation by 2 but it will be easier if you do.