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# Doug can paint a room in 5 hours. Dave can paint the same room in 7 ho

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
Doug can paint a room in 5 hours. Dave can paint the same room in 7 ho  [#permalink]

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27 Mar 2019, 00:20
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Difficulty:

55% (hard)

Question Stats:

59% (02:00) correct 41% (02:07) wrong based on 64 sessions

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Doug can paint a room in 5 hours. Dave can paint the same room in 7 hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let t be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by t?

(A) $$(\frac{1}{5} + \frac{1}{7})(t + 1) = 1$$

(B) $$(\frac{1}{5} + \frac{1}{7})t + 1 = 1$$

(C) $$(\frac{1}{5} + \frac{1}{7})t = 1$$

(D) $$(\frac{1}{5} + \frac{1}{7})(t - 1) = 1$$

(E) $$(5 + 7)t = 1$$

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Doug can paint a room in 5 hours. Dave can paint the same room in 7 ho  [#permalink]

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Updated on: 27 Mar 2019, 01:45
Bunuel wrote:
Doug can paint a room in 5 hours. Dave can paint the same room in 7 hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let t be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by t?

(A) $$(\frac{1}{5} + \frac{1}{7})(t + 1) = 1$$

(B) $$(\frac{1}{5} + \frac{1}{7})t + 1 = 1$$

(C) $$(\frac{1}{5} + \frac{1}{7})t = 1$$

(D) $$(\frac{1}{5} + \frac{1}{7})(t - 1) = 1$$

(E) $$(5 + 7)t = 1$$

rate of D = 1/5 and D= 1/7
together rate ; 1/5+1/7
time = t-1 ; as it includes lunch break
work = 1
so 1= (1/5+1/7)* (t-1)
$$(\frac{1}{5} + \frac{1}{7})(t - 1) = 1$$
IMO D

Originally posted by Archit3110 on 27 Mar 2019, 01:27.
Last edited by Archit3110 on 27 Mar 2019, 01:45, edited 1 time in total.
Intern
Joined: 27 Sep 2018
Posts: 37
Re: Doug can paint a room in 5 hours. Dave can paint the same room in 7 ho  [#permalink]

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27 Mar 2019, 01:42
Rate of doing work of dave=1/7
Rate of doing work of Doug=1/5
Total time taken including lunch to complete work =t
Total time taken excluding lunch to complete work=t-1
Therefore,1/7+1/5=1/(t-1)
(1/7+1/5)(t-1)=1

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Joined: 15 Nov 2017
Posts: 52
Re: Doug can paint a room in 5 hours. Dave can paint the same room in 7 ho  [#permalink]

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05 Apr 2019, 07:29
Hello,

Could someone explain why the one-hour lunch break is considered in the original ((1/5)+(1/7)) combined rate calculation? I do not understand how D is correct since that would mean we need to remove the 1 hour from their combined rate (given) which does not include the one hour in the first place.

Any insight would be great!

KHow

Bunuel wrote:
Doug can paint a room in 5 hours. Dave can paint the same room in 7 hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let t be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by t?

(A) $$(\frac{1}{5} + \frac{1}{7})(t + 1) = 1$$

(B) $$(\frac{1}{5} + \frac{1}{7})t + 1 = 1$$

(C) $$(\frac{1}{5} + \frac{1}{7})t = 1$$

(D) $$(\frac{1}{5} + \frac{1}{7})(t - 1) = 1$$

(E) $$(5 + 7)t = 1$$
Intern
Joined: 27 Sep 2018
Posts: 37
Doug can paint a room in 5 hours. Dave can paint the same room in 7 ho  [#permalink]

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09 Apr 2019, 02:01
[quote="KHow"]Hello,

Could someone explain why the one-hour lunch break is considered in the original ((1/5)+(1/7)) combined rate calculation? I do not understand how D is correct since that would mean we need to remove the 1 hour from their combined rate (given) which does not include the one hour in the first place.

Any insight would be great!

KHow

Doug can paint a room in 5 hours. Dave can paint the same room in 7 hours.
Doug and Dave paint the room together and

take a one-hour break for lunch. ----------------- here they take one hour lunch break

Let t be the total time, in hours, required for them to complete the job working together, including lunch. --------- here total time include lunch also

Which of the following equations is satisfied by t?
Doug can paint a room in 5 hours. Dave can paint the same room in 7 ho   [#permalink] 09 Apr 2019, 02:01
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