intermediate algebra differences

Question

ot takes an older printing press 5 hours longer to complete a print job than a newer printing press. if the printing presses work together, they can complete the job in 2 hours. how long does it take each press to complete the job working alone?

Answer 1

Let x = time it takes the new printing press to complete the job. Then x+5 = time it takes the old printing press to complete the job.

 

 

Combined, the printing presses take 2 hours to complete 1 job. That means they work at a rate of 1 job per 2 hours, or 1/2 a job per hour.

 

The rate the new printing press works is 1/x jobs per hour, since it completes 1 job in x hours. The rate the old printing press works is 1/(x+5) jobs per hour, since it completes 1 job in x+5 hours.

 

 

Their combined rate should equal 1/2 a job per hour. So:

 

1/2 = 1/x + 1/(x+5)

1/2 = (x+5)/(x(x+5)) + x/(x(x+5))

1/2 = ((x+5)+x) / (x(x+5))

1/2 = (2x+5) / (x(x+5))

1 = (2(2x+5)) / (x(x+5))

1 = (4x+10) / (x(x+5))

x(x+5) = 4x + 10

x² + 5x = 4x + 10

x² + x - 10 = 0

 

 

Using the quadratic formula to solve for x, you'll get:

 

x = 2.7 OR x = -3.7

 

 

Time can't be negative, so the newer printing press takes x = 2.7 hours and the older printing press takes x+5 = 2.7+5 = 7.7 hours.