Discussion
If two workers can assemble a car in 8 hours and a third worker can assemble the same car in 12 hours, then how long would it take the three workers together to assemble the car?
| (A) | |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 11/07/2012 09:10
Of the formula would be time= Work/rate, why divide 1/fraction work? Could you expolian further?
Posted: 11/13/2012 01:23
Hi Daniela,
This is a difficult and non-intuitive problem, so don't feel bad. Sometimes it's useful to spell it out using English:
Productivity rate of workers 1 and 2: 1 car per 8 hours, or 1/8 car per hour
Productivity rate of worker 3: 1 car per 12 hours, or 1/12 car per hour
The blended rate of workers 1&2 and worker 3 is (1/8 + 1/12) car per hour, or 5/24 car per hour. Hence, to assemble 1 car using the 3 workers, we need:
Productivity rate = # cars divided by time
5/24 = 1 divided by x hours
x = 1 divided by 5/24 = 24 / 5 = 4 4/5 hours
This is a difficult and non-intuitive problem, so don't feel bad. Sometimes it's useful to spell it out using English:
Productivity rate of workers 1 and 2: 1 car per 8 hours, or 1/8 car per hour
Productivity rate of worker 3: 1 car per 12 hours, or 1/12 car per hour
The blended rate of workers 1&2 and worker 3 is (1/8 + 1/12) car per hour, or 5/24 car per hour. Hence, to assemble 1 car using the 3 workers, we need:
Productivity rate = # cars divided by time
5/24 = 1 divided by x hours
x = 1 divided by 5/24 = 24 / 5 = 4 4/5 hours