Another QR problem

[sacjumpman]

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Josh and Jennifer start at the same time and together paint their apartment in 3 hours.

Jennifer always rests for 5 minutes after painting for 20 minutes, and Josh always rests for 5 minutes after painting for 30 minutes.

Which is greater?
Column A
One-half the number of minutes they work together

Column B
The number of minutes they don't work together

Answer choices:
A: Column A is bigger
B: Column B is bigger
C: They are equal
D: Not enough info

I was just curious if anyone had any quick techniques for this problem. My way is very, very slow. I'd have to skip this on the real test.

No explanation was given for this particular problem. But the correct answer is highlighted in red.

Thanks in advance to all.

 

[Mstoothlady2012]

I would use formula 1/rate1 + 1/rate2 = 1/total rate

1/20 + 1/30 = 1/total rate
total rate = 12

one half that number = 12/2 = 6

So they work together for 6 minutes and within those 6 mins no1 will take a break. So i guess the answer is A

I hope that make sense!

Josh and Jennifer start at the same time and together paint their apartment in 3 hours.

Jennifer always rests for 5 minutes after painting for 20 minutes, and Josh always rests for 5 minutes after painting for 30 minutes.

Which is greater?
Column A
One-half the number of minutes they work together

Column B
The number of minutes they don't work together

Answer choices:
A: Column A is bigger
B: Column B is bigger
C: They are equal
D: Not enough info

I was just curious if anyone had any quick techniques for this problem. My way is very, very slow. I'd have to skip this on the real test.

No explanation was given for this particular problem. But the correct answer is highlighted in red.

Thanks in advance to all.

 

[Streetwolf]

Josh's cycle repeats every 35 minutes (30 + 5 break) and Jennifer's cycle repeats every 25 minutes (20 + 5 break). They start at the same time so already that's 20 minutes working together.

First find the LCM of 25 and 35. It is 175. So we have 25*7 = 175 and 35*5 = 175. Thus, if the two people keep repeating their cycles, they will eventually start at the same time again after 175 minutes. Since they take their breaks at the end of their cycle, they both take a break from 170-175 minutes. Every other time they break, they break alone. Since they work for 3 hours, they work for 180 minutes.

How many breaks do they get?

Josh works 30 minutes for every 35. Since he works 5 complete cycles, he gets 5 breaks = 5*5 = 25 minutes of break time.

Jennifer works 20 minutes for every 25. Since she works 7 complete cycles, she gets 7 breaks = 7*5 = 35 minutes of break time.

But they both take the last break together, so you only count one of those last breaks. Thus you have 25 + 35 = 60 minutes - 5 minutes (shared break, only count it once) = 55 minutes of break time.

They worked for 180 minutes so if they weren't working together for 55 minutes they must be working together for 180-55 = 125 minutes. Choice A wants half of this time = 62.5 minutes. Choice B wants the break time = 55 minutes. Clearly choice A > choice B.

***Be careful of choice C***

Had you not subtracted that 5 minutes of shared break time (since it was counted twice), you would have had 60 minutes of break time. Since they worked 180 minutes, you would have done 180-60 = 120 minutes working together. So column A would be 120/2 = 60. Column B would also be 60. You'd have chosen C. But that is wrong!!

 

[Flipper405]

Josh's cycle repeats every 35 minutes (30 + 5 break) and Jennifer's cycle repeats every 25 minutes (20 + 5 break). They start at the same time so already that's 20 minutes working together.

First find the LCM of 25 and 35. It is 175. So we have 25*7 = 175 and 35*5 = 175. Thus, if the two people keep repeating their cycles, they will eventually start at the same time again after 175 minutes. Since they take their breaks at the end of their cycle, they both take a break from 170-175 minutes. Every other time they break, they break alone. Since they work for 3 hours, they work for 180 minutes.

How many breaks do they get?

Josh works 30 minutes for every 35. Since he works 5 complete cycles, he gets 5 breaks = 5*5 = 25 minutes of break time.

Jennifer works 20 minutes for every 25. Since she works 7 complete cycles, she gets 7 breaks = 7*5 = 35 minutes of break time.

But they both take the last break together, so you only count one of those last breaks. Thus you have 25 + 35 = 60 minutes - 5 minutes (shared break, only count it once) = 55 minutes of break time.

They worked for 180 minutes so if they weren't working together for 55 minutes they must be working together for 180-55 = 125 minutes. Choice A wants half of this time = 62.5 minutes. Choice B wants the break time = 55 minutes. Clearly choice A > choice B.

***Be careful of choice C***

Had you not subtracted that 5 minutes of shared break time (since it was counted twice), you would have had 60 minutes of break time. Since they worked 180 minutes, you would have done 180-60 = 120 minutes working together. So column A would be 120/2 = 60. Column B would also be 60. You'd have chosen C. But that is wrong!!

Very good. 👍 Hopefully, the actual test won't have anything this difficult, but it's good practice.

 

[sacjumpman]

Josh's cycle repeats every 35 minutes (30 + 5 break) and Jennifer's cycle repeats every 25 minutes (20 + 5 break). They start at the same time so already that's 20 minutes working together.

First find the LCM of 25 and 35. It is 175. So we have 25*7 = 175 and 35*5 = 175. Thus, if the two people keep repeating their cycles, they will eventually start at the same time again after 175 minutes. Since they take their breaks at the end of their cycle, they both take a break from 170-175 minutes. Every other time they break, they break alone. Since they work for 3 hours, they work for 180 minutes.

How many breaks do they get?

Josh works 30 minutes for every 35. Since he works 5 complete cycles, he gets 5 breaks = 5*5 = 25 minutes of break time.

Jennifer works 20 minutes for every 25. Since she works 7 complete cycles, she gets 7 breaks = 7*5 = 35 minutes of break time.

But they both take the last break together, so you only count one of those last breaks. Thus you have 25 + 35 = 60 minutes - 5 minutes (shared break, only count it once) = 55 minutes of break time.

They worked for 180 minutes so if they weren't working together for 55 minutes they must be working together for 180-55 = 125 minutes. Choice A wants half of this time = 62.5 minutes. Choice B wants the break time = 55 minutes. Clearly choice A > choice B.

***Be careful of choice C***

Had you not subtracted that 5 minutes of shared break time (since it was counted twice), you would have had 60 minutes of break time. Since they worked 180 minutes, you would have done 180-60 = 120 minutes working together. So column A would be 120/2 = 60. Column B would also be 60. You'd have chosen C. But that is wrong!!

Continuously impressed. 👍

Thank you.

 

[Mstoothlady2012]

Josh's cycle repeats every 35 minutes (30 + 5 break) and Jennifer's cycle repeats every 25 minutes (20 + 5 break). They start at the same time so already that's 20 minutes working together.

First find the LCM of 25 and 35. It is 175. So we have 25*7 = 175 and 35*5 = 175. Thus, if the two people keep repeating their cycles, they will eventually start at the same time again after 175 minutes. Since they take their breaks at the end of their cycle, they both take a break from 170-175 minutes. Every other time they break, they break alone. Since they work for 3 hours, they work for 180 minutes.

How many breaks do they get?

Josh works 30 minutes for every 35. Since he works 5 complete cycles, he gets 5 breaks = 5*5 = 25 minutes of break time.

Jennifer works 20 minutes for every 25. Since she works 7 complete cycles, she gets 7 breaks = 7*5 = 35 minutes of break time.

But they both take the last break together, so you only count one of those last breaks. Thus you have 25 + 35 = 60 minutes - 5 minutes (shared break, only count it once) = 55 minutes of break time.

They worked for 180 minutes so if they weren't working together for 55 minutes they must be working together for 180-55 = 125 minutes. Choice A wants half of this time = 62.5 minutes. Choice B wants the break time = 55 minutes. Clearly choice A > choice B.

***Be careful of choice C***

Had you not subtracted that 5 minutes of shared break time (since it was counted twice), you would have had 60 minutes of break time. Since they worked 180 minutes, you would have done 180-60 = 120 minutes working together. So column A would be 120/2 = 60. Column B would also be 60. You'd have chosen C. But that is wrong!!

so if i do it my way i would have gotten it wrong? did i just get lucky for this prob and got the right answer? or does that method apply to all the similar probs?

thanks!

 

[Streetwolf]

Yeah you got lucky. Rate problems apply when you need to know how long they worked together for. The problem already told you.

 

[jay47]

Wow, streetwolf, i looked at your predent stats and I think you are the only person the year you took the test to get an AA of 26...impressive but believable given you know how to do every math problem people throw at you. Thanks for the help btw.