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When working independently, machine A can complete a piece of work in

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When working independently, machine A can complete a piece of work in  [#permalink]

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New post 13 Feb 2019, 06:13
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When working independently, machine A can complete a piece of work in 10 hours, and machine B can complete the same wok in 6 hours. Both machines worked together for 3 hours, and then Machine A stopped working. How much more time did machine B take to complete the remaining work ?

    A. 1 hour
    B. 1 hours 12 minutes
    C. 1 hour 20 minutes
    D. 1 hour 48 minutes
    E. 2 hours


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Re: When working independently, machine A can complete a piece of work in  [#permalink]

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New post 13 Feb 2019, 06:19
ra = 1/10 ; rb= 1/6
combined rate = 16/60 ; 4/15

combined work done in 3 hrs = 4 * 3 /15 = 4x/5
left x/5
so time taken by B
x/5 * 6= time
x=1
1.2 hrs or say 1.2* 60= 72 mins ~ 1 hr 12 mins IMO B

EgmatQuantExpert wrote:
When working independently, machine A can complete a piece of work in 10 hours, and machine B can complete the same wok in 6 hours. Both machines worked together for 3 hours, and then Machine A stopped working. How much more time did machine B take to complete the remaining work ?

    A. 1 hour
    B. 1 hours 12 minutes
    C. 1 hour 20 minutes
    D. 1 hour 48 minutes
    E. 2 hours


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Re: When working independently, machine A can complete a piece of work in  [#permalink]

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New post 13 Feb 2019, 22:03
1
work done by A in 1 hour = \(\frac{1}{10}\)

work done by B in 1 hour = \(\frac{1}{6}\)

work done by A and B in 1 hour = \(\frac{1}{10}\) + \(\frac{1}{6}\)

= \(\frac{16}{60}\)

They worked together for 3 hours. So \(3*\frac{16}{60}\)

\(\frac{16}{20}\)

Remaining work is \(\frac{4}{20}\)

Now A stopped working and B has to complete the work.

\(x*\frac{1}{6}\) = \(\frac{4}{20}\)

x = \(\frac{24}{20}\)

x = \(\frac{24}{20}*60\) minutes

x = 72 minutes or 1 hour 12 minutes.

OPTION: B
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Re: When working independently, machine A can complete a piece of work in  [#permalink]

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New post 14 Feb 2019, 22:11
LCM is 60, so it is equivalent to say that:
A produces 6 units every hour
B produces 10 units every hour

So in 3 hours we have 3(6+10) = 48 units of 60
So B needs to produce 12 remaining units in x hours

10 units in 1 hour
12 units in x hour
x = 1,2 hour or 1hour and 12 min
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Re: When working independently, machine A can complete a piece of work in  [#permalink]

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New post 14 Feb 2019, 22:36

Solution



Given:
In this question, we are given
    • Working independently, machine A can complete a piece of work in 10 hours.
    • Working independently, machine B can complete a piece of work in 6 hours.
    • Both machines worked together for 3 hours, and then machine A stopped working.
    • The remaining work was completed by machine B, working alone.

To find:
We need to determine
    • The extra time taken by machine B, to complete the remaining work.

Approach and Working:
Let us assume the total work to be the LCM (10, 6, 3) = 30 units

In 10 hours, machine A does 30 units of work.
    • Hence, in 1 hour, machine A does \(\frac{30}{10}\) = 3 units of work

In 6 hours, machine B does 30 units of work.
    • Hence, in 1 hour, machine B does \(\frac{30}{6}\) = 5 units of work

In 1 hour, machine A and machine B together can finish (3 + 5) = 8 units

As they worked for 3 hours together, total work completed in those 3 hours = (8 x 3) units = 24 units.
    • Remaining work after 3 hours = (30 – 24) units = 6 units

As machine B completed the remaining work alone, the extra time taken beyond 3 hours = \(\frac{6}{5}\) hours = 1 hour 12 minutes.

Hence the correct answer is Option B.

Answer: B


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Re: When working independently, machine A can complete a piece of work in  [#permalink]

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New post 18 Feb 2019, 18:10
EgmatQuantExpert wrote:
When working independently, machine A can complete a piece of work in 10 hours, and machine B can complete the same wok in 6 hours. Both machines worked together for 3 hours, and then Machine A stopped working. How much more time did machine B take to complete the remaining work ?

    A. 1 hour
    B. 1 hours 12 minutes
    C. 1 hour 20 minutes
    D. 1 hour 48 minutes
    E. 2 hours



Machine A’s rate is 1/10, and machine A worked for 3 hours. Machine B’s rate is 1/6. If we let n = the extra time that machine B worked, then machine B worked for (3 + n) hours. We can create the equation:

(1/10)(3) + (1/6)(3 + n) = 1

3/10 + (3+n)/6 = 1

Multiplying by 30, we have:

9 + 15 + 5n = 30

5n = 6

n = 6/5 = 1 1/5 = 1 hour and 12 minutes.

Alternate Solution:

Working alone, Machine A and Machine B can complete 1/10 and 1/6 of the job in one hour, respectively. Together, they complete 1/10 + 1/6 = 16/60 = 4/15 of the job in one hour. Since they work for 3 hours, 3 x 3/15 = 12/15 = 4/5 of the job is completed and 1 - 4/5 = 1/5 of the job remains. Since Machine B completes the whole job in 6 hours, it will complete 1/5 of the job in 6 x 1/5 = 6/5 hours or, equivalently, 1 hour and 12 minutes.

Answer: B
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Re: When working independently, machine A can complete a piece of work in   [#permalink] 18 Feb 2019, 18:10
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