tim can shell a bushel of peas in 2 hours. jill can shell a bushel in 3 hours. how long will it take them to shell a bushel of peas if they work together

Question

tim can shell a bushel of peas in 2 hours. jill can shell a bushel in 3 hours. how long will it take them to shell a bushel of peas if they work together

Answer 1

Tim takes 2 hours so he does 1/2 bushel per hour

Jill takes 3 hours so she does 1/3 bushel per hour

 

Together they do 1/2 + 1/3 = 5/6 bushels per hour

You set the equation up as:

(5/6 per hour)(h hours) = 100%

 

(5/6)h = 1

h = 6/5 = 1 1/5 hours or 1 hour 12 minutes

 

Note: (1/5 hr)(60 min/hr) = 12 minutes

Answer 2

The key to these types of problems is that when two or more folks work together, it is their rates of doing work that we want to add.    If time can shell a bushel of peas in 2 hours, his rate is 1 bushel/2 hours.   Jills rate is 1 bushel/3 hours.

 

Combined they can shell 1/2 + 1/3 or  0.666667 bushels per hour.   Now we can calculate the time required to shell one bushel.  W = R*T     T = 1bushel/0.666667bph = 1.5 bushels.