VeritasKarishma wrote:
Work Rate problems are based on the concept that rates are additive. That is to say that if I paint half a wall in an hour and if you paint half a wall in an hour, if we both work together on a wall, we will finish the wall in an hour (Assuming that you are not repainting whatever I am painting to cover up my shoddy work!).
Remember, Rate of work = Work done per unit time
So, the proper way to express rate is 1/2 wall per hour and not 1 wall in 2 hours
If my rate of work is 1/2 wall/hour and yours is 1/2 wall/hour, our total rate of work is 1/2 + 1/2 = 1 wall/hour.
The basic questions of work rate are of the following form:
If A, working independently, completes a job in 10 hours and B, working independently, completes a job in 5 hours, how long will they take to complete the same job if they are working together?
Since A completes a job in 10 hours, his rate of work is 1/10th of the job per hour. B's rate of work is 1/5th of the job per hour.
Their combined rate of work would then be 1/10 + 1/5 = 3/10th of the job per hour.
As we said before, Rate of work = Work done/Time so 3/10 = 1/T (because 1 job has to be done)
or T = 10/3 hours.
This implies that A and B will together take 3.33 hours to do the job.
Note: Time taken when A and B work together will obviously be less than time taken by A or B when they are working independently.
Coming back to your question (finally! I know!), if A takes 5 hours to fill a lot and B takes x hours, and together they fill it in 2 hours, what is x?
Rate of work of A = 1/5th of the lot per hour
Rate of work of B = 1/xth of the lot per hour
Combined rate of work = 1/2 of the lot per hour
1/2 = 1/5 + 1/x
x = 10/3 hours
Note: Without solving, I know that E cannot be the answer since they both together take 2 hours to complete the work so one person alone can definitely not do the work in less than 2 hours.
Time for a Teaser: A and B, working together, can finish a job in 10 days, B and C, working together, can finish the same job in 12 days and A and C, working together, can finish the same job in 15 days. If all three work together, how long will they take to finish the same job?
Hi Karishma,
The explanation was wonderful. I tried to solve the teaser and my answer is 4 days. Is it correct?