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A type A machine can complete a job in 5 hours and a type B machine ca

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A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 21:19
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A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 21:30
1
let the total work would be 35 units (LCM of 5 & 7)
Since type A machine takes 5 hours to complete the work, A machine does 7 units of work per hour.
Similarly, type B machine does 5 units of work per hour.
Now, work done per hour by 2 type A machines and 3 type B machines working together
= 2*7+3*5 = 14+15= 29 units
time taken = total work required/work done per hour = 35/29 = D
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 21:31
1
Ta=5hrs, Tb=7hrs
We are to find how long 2 machine As and 3 machine Bs can finish the work working together.

I/Tc = 1/5 + 1/5 + 1/7 + 1/7 + 1/7 = 2/5 + 3/7 = 29/35
Hence Tc = 35/29.

The answer is therefore option D in my view.

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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 21:42
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Formula: Work = Rate*time

Let the total work = LCM (5, 7) = 35 units

Rate of A, \(R_A = \frac{35}{5} = 7 u\)nits/hr &
Rate of B, \(R_B = \frac{35}{7} = 5\) units/hr

Rate of 2 type A & 3 type B = \(2*R_A + 3*R_B\) \(= 2*7 + 3*5 = 29\)

--> Time taken = Work/Rate = \(\frac{35}{29}\)

IMO Option D
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 21:43
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2A machines can do 2/5 of a job in one hour.
3B machines can do 3/7 of a job in one hour.
So, (2/5 + 3/7)X=1
X=35/29
Option D

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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 21:53
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Together time = x
2/A + 3/B = 1/x
2/5 + 3/7 = 1/x
29/35 =1/x
x = 35/29

OA:D

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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 21:54
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Assume total work= LCM(5,7)=35 units

Type A machine can do 7 units/hour
Type B machine can do 5 units/hour

Total time taken by 2 type A machines and 3 type B machines working together= \(\frac{35}{(2*7+3*5)}\)= \(\frac{35}{29}\) hours

D
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 22:17
1
1
A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

Work done by type A machine in 1 hour = 1/5
Work done by type B machine in 1 hour = 1/7

Work done by 2 type A machines and 3 type B machines in 1 hour = 2/5 + 3/7 = (14+15)/35 = 29/35

Hours taken by 2 type A machines and 3 type B machines to complete the job = 35/29 hours

IMO D
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 17 Oct 2019, 22:55
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A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

Work done in 1 hour by a Type A machines = \(\frac{1}{5}\) units
Work done in 1 hour by 2 Type A machines = \(\frac{2}{5}\) units

Work done in 1 hour by a Type B machines = \(\frac{1}{7}\) units
Work done in 1 hour by 3 Type B machines = \(\frac{3}{7}\) units

Work done in 1 hour by 2 Type A and 3 Type B machines = \(\frac{2}{5} + \frac{3}{7}\) = \(\frac{29}{35}\) units
Thus time taken to complete the job by the five machines = \(\frac{1}{29/35}\) = \(\frac{35}{29}\) hours

IMO Answer D.
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 18 Oct 2019, 01:04
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A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

A machine complete a job in 5 hours, so in 1 hour A machine can complete 1/5 of jobs.
B machine complete a job in 7 hours, so in 1 hour B machine can complete 1/7 of jobs.

2 A machines, can complete 2/5 jobs per hour
and 3 B machines, can complete 3/7 jobs per hour

working together, they can complete 2/5 + 3/7 = 29/35

Thus, it requires 1/ (29/35) = 35/29 hours to complete the job.

Therefore D is the correct answer
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 18 Oct 2019, 01:37
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rate of A; 1/5 and rate of B ; 1/7
rate of 2 A and 3 B ; 2/5 and 3/7
together rate ; 2/5+3/7 =29/35 ; time ; 35/29
IMO D


A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 18 Oct 2019, 02:03
1
Quote:
A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12


Rate=\(\frac{Work}{Time taken}\)

Let the required work to do be 1 unit.

So, rate of doing work of machine A=\(\frac{1}{5}\)
Thus, rate of doing work of 2 machine A=\(\frac{2}{5}\)
Similarly, rate of doing work of machine B=\(\frac{1}{7}\)
Thus, rate of doing work of 3 machine B=\(\frac{3}{7}\)

Total rate= \(\frac{2}{5}+\frac{3}{7}\)=\(\frac{29}{35}\)
So, Total time=1/29/35=\(\frac{35}{29}\)

Thus, the correct answer is option D.
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 18 Oct 2019, 06:36
1
Quote:
A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12


rate=job*time, rA=1/5, rB=1/7

job/rate=time, 1/(2a+3b)=t, 1/(2/5+3/7)=t, t=35/29

Answer (D)
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 18 Oct 2019, 13:14
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a type A machine —\(\frac{1}{5}\)
a type B machine—\(\frac{1}{7}\)
———————
\(2( \frac{1}{5})+ 3( \frac{1}{7})\)= \(\frac{1}{x}\) ???

—> \(\frac{2}{5}+ \frac{3}{7}\)= \(\frac{(14+ 15)}{35}\)=\(\frac{1}{x}\)
—> x = \(\frac{35}{29}\)

The answer is D.

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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 18 Oct 2019, 22:04
1
A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

(1/5)+(1/7)=12/35--rate
time is reciprocal of rate, therefore, 35/12 hours for 1A and 1B

2A and 3B
2/5+3/7=14/35+15/35=29/35
reciprocal = 35/29
Therefore, D
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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New post 18 Oct 2019, 22:15
1
A complete the 1/5 of work in one hour and B 1/7 in one hour.

so 2A+ 3B in one hour is (2/5+3/7) of work
==> 29/35 work in one hour
==> total work in 1/(29/35) = 35/29

Ans:: D

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Re: A type A machine can complete a job in 5 hours and a type B machine ca   [#permalink] 18 Oct 2019, 22:15
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