Workers A and B working together can finish a job in 8 hrs.If they work together for 6 hrs.,after which worker A leaves,then worker B needs 9 more hrs to finish the job.How long does it take worker A to do the job alone?
1/A + 1/B = 1/8
... 15/B = 15/8 - 15/A
6/A + 15/B = 1
... 6/A - 15/A + 15/8 = 8/8
... -9/A = -7/8
... -72 = -7A
or, equivalently,
1/A + 1/B = 1/8
6/8 + 9/B = 1
To solve this problem, we can set up an equation based on the given information.
Let's assume that worker A takes x hours to complete the job alone.
Since worker A and worker B working together can finish the job in 8 hours, their combined work rate is 1 job per 8 hours. Therefore, their combined work rate is given by:
1/(8) = 1/x + 1/(8-x)
Now, we can solve this equation to find the value of x.
Multiply both sides of the equation by 8x(8-x) to eliminate the denominators:
8x(8-x)/8 = 8x(8-x)/x + 8x(8-x)/8
Simplifying the equation:
8(8-x) = 8(8) + x(8-x)
64 - 8x = 64 + 8x - x^2
Rearranging the equation:
x^2 - 16x = 0
Factoring out x:
x(x - 16) = 0
Setting each factor equal to zero and solving for x:
x = 0 or x - 16 = 0
Since it doesn't make sense for it to take 0 hours for worker A to finish the job alone, we will disregard that solution.
Therefore, x - 16 = 0, which gives us:
x = 16
So, it takes worker A 16 hours to complete the job alone.