Bunuel wrote:
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. \(4\)
This is an excelent question to plug in some numbers , and solve it less then a minute !
FIrst lets think about good number that the work can take, 50 ! (as a multiple of both 5, and 10).
Now if the total Job is 50 (imagine it is a big wall that need 50 litter of paint), lets find out the work speed of each worker:
A: 50/10 = 5
B: 50/5 = 10.
C: i will leave it as it is .
Now:
worker A works 4+1/4 hours *5(his work speed) = 21.25
worker B works 2+1/4 Hours * 10(his work speed) = 22.5
the work that left for worker C is 50-43.75=6.25 (because he worked only 1/4 hours lets multiple that by 4 to get is speed in a hour) *4=25 (we got now his work speed )
To caculate the time for X = 50/25= 2