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64% (02:44) correct 36% (03:27) wrong based on 115 sessions
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Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of \(x\)?
Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of \(x\)?
A. \(1\) B. \(1.25\) C. \(2\) D. \(2.5\) E. \(4\)
After 2 hours \(2*\frac{1}{10}=\frac{1}{5}\) of the taks will be done (as only A works);
After 4 hours \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task will be done and \(\frac{1}{5}\) will be left to be done;
We are told that 1/5th of the task is done in 15 minutes (1/4th of an hour) by all three workers: \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\). From which we can find that \(x=2\) hours.
Consider the total work as 10, and A can do 1 work in 1hr, B can do 2 work in 1 hr. A starts work for 2 hrs. So 2 work completed(1×2=2), then B joins for 2 hrs, so B does 4 work (2×2=4), now total work = A's 4+B's 4 work = 8. Balance work is 2. C joins and complete the work in 15 mins. That is A do .25 work and B do .5 work in15 mins., total .75 work(.25+.5=.75).Balace 1.25 work is done by C in 15 mins. So C can do 5 work in 1 hr. It means C takes 2hrs to complete the total work. Ans : opt.c, 2hrs
A - 10 hours to complete the work B- 5 hours to complete the work C- X hours to complete the work Take the LCM of 10,5,x = 10x (total work) Hence A rate of work = 10x/10 = X units/hour B rate of work = 10x/5 = 2x units/hour C rate of work = 10x/x = 10 units/hour therefore X*2 +(2x+x)*2+(2x+x+10)*1/4 =10x this gives X =2 (quick and easy)
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I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you
Why is the question of poor quality? That's not right. Both the question and the solution are correct and detailed enough.
After you get \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\), only simple algebraic manipulations are left to be done:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you
Why is the question of poor quality? That's not right. Both the question and the solution are correct and detailed enough.
After you get \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\), only simple algebraic manipulations are left to be done:
I think this is a high-quality question and I agree with explanation. I feel we take too long to answer this kind of question (in general), despite being simple math.
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64% (02:44) correct 
