How long would it take the machines to complete the job?

Question

Machine A can do a job 12 hours and machine B can do the job in 8 hours.

If B starts 2 hours after A has started, find the total time needed for the two machines to complete the job?


Please explain >< !!!

Answer 1

___________Machine A_____Machine B
Time (h)______12___________8
Rate of work__X/12_________X/8
(units / h)

After 2 h, work done by A = X/6 units
Remaining work = 5X/6 units

Working together, the rate of work is:-
X/12 + X/8 = 5X/24 units

Time = (5X/6) / (5X/24) h
Time = (5X/6) x (24 / 5X) h
Time = 4 h

Will take 4 hours after they start working together.

But B worked for 2 hours beforehand.

Total = 6 h

Answer 2

Here's another way of looking at it:

Since it takes Machine A 12 hours to complete a full job, Machine A completes 1/12 of the job every hour.

Since it takes Machine A 8 hours to complete a full job, Machine B completes 1/8 of the job every hour.

In the first two hours: A does 0, B does 2/12
Hour3: A does 1/8, B does 1/12
Hour4: A does 1/8, B does 1/12
Hour5: A does 1/8, B does 1/12
Hour6: A does 1/8, B does 1/12

Totaling A's amount of the job gives you (1/8 + 1/8 + 1/8 + 1/8) = 4/8 = 1/2

Totaling B's amount of the job gives you (2/12 + 1/12 + 1/12 + 1/12 + 1/12) = 6/12 = 1/2

A's 1/2 of the job + B's 1/2 of the job gives you the whole job. Therefore, the total time it takes both machines to finish the job is 6 hours.

Answer 3

Machine A completes 1/12 of the job every hour
Machine B completes 1/8 of the job every hour

Working together, machines A and B complete 1/12 + 1/8 = 5/24 of the job every hour

Machine A works for 2 hours and completes 1/6 of the job
5/6 of the job is left

(5/6)/(5/24) = 24/6 = 4

Machines A and B would require 4 more hours to complete the rest of the job.

Taking into account the original 2 hours, the total time required to complete the job is 6 hours.

Answer 4

working alone, A will have done 1/12x2 = 1/6 part of the job. the work done here is equal to the rate (for A, this is 1 job in 12 hours, or 1/12) times the time, which is 2 hours. hence, A does 1/6 of the job alone in the first part.
when B comes in, both A and B work together, so that the work they do together ought to be 5/6 of the total job. If we let x be the time they work together to complete the rest of the job, then the work of A = (1/12 times x), and the work of B is (1/8 times x), and so we have:
1/12x + 1/8x = 5/6
simplifying by multiplying both sides of the equation by the LCD = 24, we get
3x + 2x = 20, and x =4 hours. The total time to do the job (from the start when A started alone) is thus 2+4 = 6 hours.

Answer 5

A does 1/12 of the job an hour
B does 1/8 of the job an hour

After 2 hours, A will have completed 2 * 1/12 = 1/6 of the job. That leaves 5/6 to be done.

Let T be the number of hours remaining:
(1/12 + 1/8)T = 5/6

Multiply everything by 24 to get rid of denominators:
(2 + 3)T = 20
5T = 20
T = 4

So A will work alone for 2 hours, then A and B will work together for 4 more hours ---> total of 6 hours.

Answer 6

Let t = time to complete the job after machine B had worked in 2 hours.

2(1/8) + t(1/12 + 1/8) = 1
1/4 + t(2/24 + 3/24) = 1
1/4 + 5/24t = 1
5/24t = 3/4
t = 18/5 or 3.6

Answer: 3.6 hrs or 3 hrs & 36 min after machine B had worked 2 hours.

The total time used to complete the job was: 3 hrs & 36 min for machine A and 5 hrs & 36 min for machine B.

Proof:
2(1/8) + 3.6(1/12) + 3.6(1/8) = 1
0.25 + 0.3 + 0.45 = 1
1 = 1

Machine A hrs + machine B hours = 1 job
3.6(1/12) + 5.6(1/8) = 1
0.3 + 0.7 = 1
1 = 1

Answer 7

A completes 1 job per 12h. After 2 hours, A has completed

    2h · (1job/12h) = (1/6)job

leaving (5/6) of the job to be completed.

Working together, A and B can complete

    1job/12h + 1job/8h = 5jobs/24h

A and B can complete the remaining (5/6) job in

     (5/6) job * (24h/5jobs) = 4h

Total time for job = 6h

Answer 8

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