Ms. Spinoni can prepare a mass-mailing of 500 letters in 10 hours. Mr. Harris can prepare a mass-mailing of 500 letters in 15 hours. How long will it take them to prepare a mass-mailing of 1000 letters if they work together? (Hint: The complete job is twice as big)

Question

a. 6 hours c. 12.5 hours

b. 12 hours d. 25 hours

Answer 1

her rate = 500 letters/10 hrs = 50 letters/hr
his rate = 500 letters/15 hrs = 100/3 letter/h
combined rate = 50 + 100/3 or 250/3 letters/hr

so time for 1000 letters at combined rate
= 1000/(250/3) hrs
= 1000(3/250) hrs
= 12 hrs

Answer 2

A new crew of painters takes two times as long to paint a small apartment as an experienced crew. Together, both crews can paint the apartment in 4 hours. How many hours does it take the new crew to paint the apartment?