Machine A takes 10 hours to complete a certain job and start

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ktrout2020: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Wed Oct 30, 2019 1:10 pm

Machine A takes 10 hours to complete a certain job and start

by ktrout2020 » Thu Oct 31, 2019 6:27 am

Machine A takes 10 hours to complete a certain job and starts that job at 9 am. After one hour of working alone, machine A is joined by machine B and together they complete the job at 5 pm. How long would it have taken machine B to complete the job if it had worked alone for the entire job?

(A) 15 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) 35 hours

Source: Veritas
Answer: E

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Source: Beat The GMAT — Problem Solving | Thu Oct 31, 2019 6:27 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Fri Nov 01, 2019 6:16 am

ktrout2020 wrote:Machine A takes 10 hours to complete a certain job and starts that job at 9 am. After one hour of working alone, machine A is joined by machine B and together they complete the job at 5 pm. How long would it have taken machine B to complete the job if it had worked alone for the entire job?

(A) 15 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) 35 hours

Source: Veritas
Answer: E

One approach:

Working ALONE Machine A takes 10 hours to do the job.
With Machine B's help, the job took 8 hours to complete.
So, Machine B saved Machine A 2 hours of work.

In other words, during the 7 hours that Machine B was helping, Machine B did the work that would have taken Machine A an extra 2 hours to complete.
So, it takes Machine B 7 hours to complete the same amount of work that it takes Machine A to complete in 2 hours.
So, it takes Machine B 7/2 times as long to complete what Machine A can complete

It takes Machine A 10 hours to do the job.
So, the time it takes Machine B to do the job = (10)(7/2) = 35 = E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Sat Nov 02, 2019 2:49 pm

Workdone by A in 1 hour = 1/10 hours
Work left for A and B after 1 hour = 1 - 1/10 = 9/10
Machine A could complete the whole work in 10 hours; it did 1/10 of the work in 1 hour.
Machine B joined Machine A after 1 hour.
With their combined effort, they completed 9/10 of the work in 7 hours.
Let the total time taken for machine B to complete the work = x hours
Machine B will complete 1/x of the jon in 1 hour
Total workdone by the 2 machines in 1 hour => (1/10) + (1/x) = (x+10)/10x
Workdone by the 2 machines in 7 hours to complete 9/10 of the work =>
$$\left(\frac{x+10}{10x}\cdot7\right)=\left(\frac{9}{10}\right)$$
Divide through by 7
$$\frac{x+10}{10x}=\frac{9}{10}\cdot\frac{1}{7}\ =\ \frac{9}{70}$$
By cross multiplying
70 (x + 10) = 9 (10x)
70x + 700 = 90x
20x = 700
x = 34
Therefore, it will take machine B 35 hours to finish the work alone. Hence, option E is the correct option.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Nov 03, 2019 7:31 pm

ktrout2020 wrote:Machine A takes 10 hours to complete a certain job and starts that job at 9 am. After one hour of working alone, machine A is joined by machine B and together they complete the job at 5 pm. How long would it have taken machine B to complete the job if it had worked alone for the entire job?

(A) 15 hours
(B) 18 hours
(C) 20 hours
(D) 24 hours
(E) 35 hours

Source: Veritas
Answer: E

We let n = the number of hours that it takes machine B to complete the job by itself. We know that machine A worked for 8 hours and machine B worked for 7 hours to complete the entire job. Thus, we can create the equation:

(1/10)(8) + (1/n)(7) = 1

8/10 + 7/n = 1

4/5 + 7/n = 1

7/n = 1/5

35 = n

Answer: E

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