Rate of A = 1 job / 45 hours = 1/45 job per hour
Rate of B = 1 job / 40 hours = 1/40 job per hour
Rate of C = 1 job / 30 hours = 1/30 job per hour
Combined rate = Rate of A + Rate of B + Rate of C
= 1/45 + 1/40 + 1/30
= (8/360 + 9/360 + 12/360)
= 29/360 job per hour
Work completed by A = Rate of A * Time
= (1/45) * 13
= 13/45 job
Work completed by C = Rate of C * Time
= (1/30) * 13
= 13/30 job
To solve this problem, we need to determine the combined rate at which A, B, and C complete the work. Once we have that, we can calculate the remaining work and find out how long it would take for B to complete it alone.
Let's first find the rates at which A, B, and C complete the work:
Rate of A = 1 job / 45 hours = 1/45 job per hour
Rate of B = 1 job / 40 hours = 1/40 job per hour
Rate of C = 1 job / 30 hours = 1/30 job per hour
Since they work together, their combined rate is the sum of their individual rates:
Combined rate = Rate of A + Rate of B + Rate of C
= 1/45 + 1/40 + 1/30
= (8/360 + 9/360 + 12/360)
= 29/360 job per hour
Now, let's calculate the work completed by A and C after 13 hours:
Work completed by A = Rate of A * Time
= (1/45) * 13
= 13/45 job
Work completed by C = Rate of C * Time
= (1/30) * 13
= 13/30 job
Since A and C have worked for 13 hours each, the remaining work is:
Remaining work = 1 job - (Work completed by A + Work completed by C)
= 1 - (13/45 + 13/30)
= 1 - (26/90 + 39/90)
= 1 - (65/90)
= 25/90 job
Time taken by B = Remaining work / Rate of B
= (25/90) / (1/40)
= (25/90) * (40/1)
= (25 * 40) / (90 * 1)
= 1000 / 90
≈ 11.11 hours