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)
a. 6 hours c. 12.5 hours
b. 12 hours d. 25 hours
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
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?
To find out how long it will take both Ms. Spinoni and Mr. Harris to prepare a mass-mailing of 1000 letters, we can use the concept of work rates.
First, let's calculate the work rates of Ms. Spinoni and Mr. Harris individually. Ms. Spinoni can prepare 500 letters in 10 hours, so her work rate is 500 letters / 10 hours = 50 letters per hour. Similarly, Mr. Harris can prepare 500 letters in 15 hours, so his work rate is 500 letters / 15 hours = 33.33 letters per hour (rounded to two decimal places).
Now, since the complete job is twice as big when they prepare 1000 letters, we need to add their work rates together to find the combined work rate.
Combined work rate = Ms. Spinoni's work rate + Mr. Harris's work rate = 50 letters per hour + 33.33 letters per hour = 83.33 letters per hour.
Finally, to find the time it takes to prepare 1000 letters, we can divide the number of letters by the combined work rate.
Time = Number of letters / Combined work rate = 1000 letters / 83.33 letters per hour ≈ 12 hours.
Therefore, the answer is option b. 12 hours.