SOLUTION: Al makes $30 an hour. Bill makes $20 an hour. Bill joins Al on the job four hours after Al started. They finish the job, and the total cost for labor comes to $470. How many hours

Algebra ->  College  -> Linear Algebra -> SOLUTION: Al makes $30 an hour. Bill makes $20 an hour. Bill joins Al on the job four hours after Al started. They finish the job, and the total cost for labor comes to $470. How many hours       Log On


   

Question 157043: Al makes $30 an hour. Bill makes $20 an hour. Bill joins Al on the job four hours after Al started. They finish the job, and the total cost for labor comes to $470. How many hours did each work?
By trial and error, I know that the number of hours is 11 for Al and 7 for Bill. I just need to show the work.
Al - 11 hours @ $30/hour = 330
Bill - 7 hours @ $20/hour = 140
Total = 470
Here is the equation that I came up with for figuring the number of hours each worked - where X=Al's hours and X-4 = Bill's hours. I'm fairly certain this equation is correct.
$470 = 30X + 20(x-4)
It's at this point that I get stuck. Any help would be greatly appreciated!
Found 2 solutions by jojo14344, alan22153:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Your on the ball amigo but a little bit of refinishing to do there.
Okay, let x= no. of hours they work
But you see, Al is already ahead of 4 hours, so total no. of hours for him is x%2B4 right? Then putting everything into equation:
Al=%28%2430%2Fhr%29%28x%2B4%29 plus
Bill= %28%2420%2Fhr%29%28x%29 equals
Total=$470
30%28x%2B4%29%2B20%28x%29=470
30x%2B120%2B20x=470
50x=470-120
50x=350 ---> cross%2850%29x%2Fcross%2850%29=cross%28350%297%2Fcross%2850%29
x=7hours ---------------> no. of hours Bill worked
x%2B4=7%2B4=11hours --------> no. of hours Al worked
In doubt? let's check;
Al+Bill=$470
%2830%2A11%29%2B%2820%2A7%29=470
330%2B140=470
470=470
Thank you,
Jojo

Answer by alan22153(1) About Me  (Show Source):
You can put this solution on YOUR website!
470= 30X+20(x-4)
20*x=20X, and
20*-4=-80
470=30X+20X-80 or
add 80 to each side of the equation
550=50X
x=11 Al
x-4= 7 Bill