QR Problems

[eleganteye]

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I've been working on the QR section lately, and I repeatedly miss the same types of questions. I know they should be really easy, but I can't figure out how to set them up. Can someone please set up the equations and explain your reasoning? Thanks for your help!

If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?

A: 2 hr and 24 mins

Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 90 minutes. How quickly can all three fill the pool together?

A: 15 min

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

A: 2 min and 44 s

If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?

A: 1.09 days

 

[ng26]

hey, I'm wondering, where did you get the answers to these problems because they don't seem right...at least the first one...I'm pretty sure it's supposed to be 2 2/5 hrs...or 2 hrs and 24 mins

 

[ram16]

Problem 2

If it takes the first person 30 minutes, then set up the equation like this:
T/30=1 job. Where T is the time. So solving for T it would take 30 min. Yea I know that is stupid. Take it one step further for multiple people doing the same job at different times. Take the sum of the fractional parts to complete the time.

T/30 + T/45 +T/90= 1 find the common denominator which is 90 and multiple both sides of the equation by this:

3T+2T+1T=90 solving this equation 6T=90 which is 15 minutes.

ng26 is right the answer for the first one is 3 hrs and 24 min.

 

[eleganteye]

The answers were included with the questions. It was on this site: http://www.testprepreview.com/oat_practice.htm

I actually wrote the wrong answer. It was supposed to be 2 hr and 24 mins for the first question. I edited the 1st question so it won't confuse anyone.

Thanks for helping me solve these! I was close but not quite there. I appreciate it!

 

[SonyaM]

Theres actually a very fast and easy way to solve these problems. You do the following:

(Time 1) x (Time 2)
------------------
Time 1 + Time 2

So, for example... In the first problem, you would do 4x6 = 24. Divide by 4+6 = 10. 24/10 is 2 hours with a remainder of 4/10, which when you multiply top and bottom by 6, you get 24 out of 60 minutes. Therefore you have 2 hours and 24 minutes.

You have to remember that you can only do this for two times, not three. If you get three different times, you must use the formula for the first two, then use that answer with the third one. For example, the third problem should be set up like this:

4x6
--- = 24/10 = 12/5
10


Now do this:

(12/5) x 2
---------- =
(12/5) + 2


(24/5)
-------------- =
(12/5) + (10/5)


(24/5)
--------- =
(22/5)


24/22 = 1.09
Hope that helps! 🙂

 

[EyEnStein 07]

all of these are done the same way.

Take the reciprocal and perform the necessary property (either + or -, if they are painting TOGETHER its +)

Add them together after finding LCD...then take the reciprocal of the answer. If you check old threads i posted something more informative about how to do these.

Sally 4 hours --> 1/4
John 6 hours --> 1/6
Together means +

1/4 + 1/6 = 3/12 + 2/12 = 5/12 ..

5/12 --reciprocal-->12/5 hours which is equal to 2.4 hours

EDIT:

i realize some of you might not see this. 2.4 hours means

if 1 hour is 60 mins...then how many minutes is .4 hours

1/60 = .4/x --> 24mins therefore...---> 2 hours and 24 mins.