1.8) If it takes 3 hours to print a local newspaper using four pointers. 8.1) How long will it take six printers to print the newspaper? 8.2) How many printers are needed if the printing of the paper must b completed in four hours?

Question

UpStudy AI · Accepted Answer

Let the rate at which one printer works be $$ r $$ (newspapers per hour).

1. Since 4 printers take 3 hours to print one newspaper, the combined work is given by:
   $$
   4r \times 3 = 1
   $$
   Solving for $$ r $$:
   $$
   12r = 1 \quad \Longrightarrow \quad r = \frac{1}{12}
   $$

2. For 8.1, using 6 printers, the combined rate is:
   $$
   6r = 6 \times \frac{1}{12} = \frac{6}{12} = \frac{1}{2} \quad \text{(newspaper per hour)}
   $$
   To print one newspaper, the time $$ t $$ is given by:
   $$
   \frac{1}{2}t = 1 \quad \Longrightarrow \quad t = \frac{1}{\frac{1}{2}} = 2 \quad \text{hours}
   $$

3. For 8.2, let the number of printers needed be $$ n $$. They must complete the newspaper in 4 hours, so:
   $$
   n \times r \times 4 = 1
   $$
   Substitute $$ r = \frac{1}{12} $$:
   $$
   n \times \frac{1}{12} \times 4 = 1 \quad \Longrightarrow \quad n \times \frac{4}{12} = 1 \quad \Longrightarrow \quad n \times \frac{1}{3} = 1
   $$
   Solving for $$ n $$:
   $$
   n = 3
   $$

Thus, the answers are:

- 8.1) It will take $$ 2 $$ hours for six printers to print the newspaper.
- 8.2) $$ 3 $$ printers are needed if the newspaper must be completed in $$ 4 $$ hours.
- 8.1) It will take 2 hours for six printers to print the newspaper. - 8.2) 3 printers are needed to complete the newspaper in 4 hours.

1.8) If it takes 3 hours to print a local newspaper using four pointers. 8.1) How long will it take six printers to print the newspaper? 8.2) How many printers are needed if the printing of the paper must b completed in four hours?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Arithmetic Questions