problem solving using rational equations

Question

In 5 hours, a secretary can address 100 envelopes. Another secretary can address 100 envelopes in 7 hours. How long would it take the secretaries, working together, to address 400 envelopes? (Hint: Think of addressing 400 envelopes as four 100-envelope jobs.)

Answer 1

The first secretary can do 1/5 of the job in an hour. The second secretary can do 1/7 of the job in an hour. So if they work together the can do 1/5 +1/7 of the job in 1 hour, or 12/35 of the job in 1 hour.

 

So 12/35 *J=1, so J= 35/12=2 and 11/12 hours to complete 100 envelopes. so now you can multiply this by 4 since you need 400 envelopes. 4*(35/12) = 35/3 = 11 2/3 hours or 11 hours and 40 minutes.

 

Hope this helped.

Answer 2

100/5 = 20 in an hour

100 / 7 = ¹⁰⁰/₇ in an hour

20 * ⁷/₇ = ¹⁴⁰/₇ Converted for addition

 

¹⁴⁰/₇ + ¹⁰⁰/₇ = ²⁴⁰/₇ in an hour

 

²⁴⁰/₇ x = 400

x = 400 * ⁷/₂₄₀

factor out 10:

x = 40 * ⁷/₂₄

factor out 4:

x = 10 * ⁷/₆

factor out 2:

x = 5 * ⁷/₃

x = ³⁵/₃ hours, or 11 ²/₃