Math word problem

Question

Jill and Clay have a catering business. It takes Jill 3 hours and 40 minutes to prep for their biggest job but working together, they can do it in two hours. How long would it take Clay by himself?

Numeric part of answers should be in form: ___hr ___mins

Answer 1

Tiffanique, , the key to “shared work” problems is to understand Work, Rate, and Time.

Work = Rate * Time

( w = r t )

Work is the amount of effort expended or material produced.

Rate is how fast someone can do the work ( what fraction of the work gets done in an hour. Or how many jobs per month, etc.)

Time is the amount of time it takes someone to get the job done.

If the amount of work is 1 job, then the rates and times are reciprocals:

1 = RT or R = 1/T or T = 1/R

It’s always good to define the Times and the Rates

T_J = Time for Jill to do the job

T_C = Time for Clay to do the job

Rates are reciprocals of Times

R_J = Rate at which Jill can do work

R_C = Rate at which Clay can do the work

R_J = 1/T_J

R_C = 1/T_C

We know

T_J = 3 2/3 = 11/3 hours to do the job

R_J = 1/(11/3) = 3/11

T_b = 2 hr (time for both together)

For combined work, 

1 = T ( Rj + Rc ) = T_b(1/Tj + 1/Tc)

1 = 2 (3/11 + 1/Tc)

1/2 = 3/11 + 1/Tc

1/2 - 3/11 = 1/Tc

(11-6)/22= 1/Tc

22/5 = Tc