2 QR work problems

[299678]

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that I don't understand the solution


Q1. . Two people can complete a job in 10 days. If one person tries to complete the job by taking a day rest after every 5 days a work. How many days will he complete> my calculation was 24 days, but the correct answer is 23 days


Q2. 6 men take 2 days to complete a work whereas 4 women take 4 days to complete the work. How men days will 3 men and 2 women working together take to complete the same work? correct answer is 8/3 days

 

[jay47]

that I don't understand the solution


Q1. . Two people can complete a job in 10 days. If one person tries to complete the job by taking a day rest after every 5 days a work. How many days will he complete> my calculation was 24 days, but the correct answer is 23 days


Q2. 6 men take 2 days to complete a work whereas 4 women take 4 days to complete the work. How men days will 3 men and 2 women working together take to complete the same work? correct answer is 8/3 days

Q1. Think of how many "job hours" are needed to finish a job. 2 People finish a job in 10 days, so that must be (let's assume 8 Hours a day)= 2X10X8= 160 working hours. Therefore, one man working 8 hours a day would take 160/8= 20 days to work. But after day 5 he takes a rest (+1 day) after day 11 he takes a rest (+1) after day 17 he takes a rest (+1) and then after 5 more days he is done. Add them up (and it may make more sense just to write it out this way) 5+1+5+1+5+1+5= 23 days.

Q2. For this, let's assign a rate to these values. Let's say it is a 24 hour job (multiple of 4 and 6), 24/6/2=2 hours per man/day. Now the women, 24/4/4= 1.5 hours per woman per day. 3 Men working at 2 hours per day and 2 women working at 1.5 hours per day would be (3*2) + (2*1.5)= 9 working hours for the group/day. 24 hours/ 9 hours per day= 8/3 days!

 

[299678]

Thank you
do you always convert this types of question by hours first?
does it help?

 

[jay47]

Thank you
do you always convert this types of question by hours first?
does it help?

Yes, absolutely. This way you can actually think about a real situation instead of a relative value.

The same concept applies for rates with fluids etc...like one pump can fill a pool in 3 hours while another pump can fill it in 2 hours. How fast can they both fill it?

Just assume the pool is a multiple of 3 and 2, so 6 and calculate it.

6 gallons/ 3 hours= 2 gallons an hour.

6 gallons/ 2 hours = 3 gallons an hour.

3+2 =5 gallons an hour

6 gallons/5 gallons an hour= 1.2 hours = 1 and 1/5 hours

Of course, the DAT would prolly ask for minutes just to make you work for it (or be arbitrarily time consuming...) so keep going.

60minutes and hour/ 5 = 12 minutes.

So 1 hour and 12 minutes.

Of course there is always the shortcut method...

(3*2)/(3+2) = 6/5 , too easy though!