word problem

Question

Martha can rake the leaves in her yard in 2 hours. Her younger brother can do the job in 6 hours. How long will it take them to do the job if they work? together?

Answer 1

The fraction of the whole job that Martha can do in 1 hour is 1/2; the fraction (work rate) of brother is 1/6 of entire job per hour.

 

To do 100% of job with each working for t hours: Martha does ½t and brother does (1/6)t.

 

Solve this equation: 1 = t(1/2 + 1/6)     The contributions of two workers; notice that the factor t is common.

 

Since 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3, we have  1 = (2/3)t.

 

Can you now solve for t (# of hours of work together)?