# Copiers

The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier?

Correct result:

t =  11.9 min

#### Solution:

$\dfrac{9-5}{ t-5} +\dfrac{5}{t}=1 \ \\ 4t+5(t-5)=t(t-5) \ \\ \ \\ t^2 -14t +25 =0 \ \\ \ \\ a=1; b=-14; c=25 \ \\ D = b^2 - 4ac = 14^2 - 4\cdot 1 \cdot 25 = 96 \ \\ D>0 \ \\ \ \\ t_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 14 \pm \sqrt{ 96 } }{ 2 } = \dfrac{ 14 \pm 4 \sqrt{ 6 } }{ 2 } \ \\ t_{1,2} = 7 \pm 4.89897948557 \ \\ t_{1} = 11.8989794856 \ \\ t_{2} = 2.10102051443 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (t -11.8989794856) (t -2.10102051443) = 0 \ \\ \ \\ t>5 \ \\ t = 11.9 \ \text{min}$

Our quadratic equation calculator calculates it.

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you want to convert velocity (speed) units?
Do you want to convert time units like minutes to seconds?

## Next similar math problems:

• Potatoes
Daniela and Michael would jointly dug potatoes for 7.5 hours. But if Daniela was working alone she would take 2.5 hours more as if he were working with Michael. Determine how much for the work done by Michael himself and how much Daniela herself.
• Two masons
Two masons built the garage together - it took 18 days. If they worked independently, the other would work 15 days more than the first. For how many days would build the garage each mason himhelp?
• Repairman
Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker?
• Work
The first worker would need less than 4 hours to complete the task than the other worker. In fact, both workers worked for two hours together, then the first worker did the remaining work himself. In what proportion should the remuneration of the workers
• Painters
The first team of painters would paint bridge in 15 days, the second in 10 days. After 3 days of working together second team goes out and continue only first team. How many days took second team to finish painting the bridge?
• Digging companies
Company A would dig a pit for 12 days, company B for 15 days, company C for 20 days and the company D for 24 days. Work began together companies C and D, but after three days joined them other two companies. How long took to dig a pit?
• Blueberries 2
Lenka and Martin collected eight liters of blueberries in two hours. How long will take to collect blueberries by Lenka itself, if we know that she collect all 2.5 hours less than Martin?
• Kohlrabies
The price of one kohlrabi increased by € 0.40. The number of kohlrabies that a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros.
• Workers
Workers A and B will done work together for 15 days. They worked together 13.5 days. Then A worker became ill and worker B finish the job alone for 7.5 days. If every worker was working alone, how many days took whole work for worker A and B?
• Fire tank
Whole fire tank was discharged once in 5 days by first out by second in \$n days. Once firefighters pumped out 6/13 of water out from the tank and then let the water flow out both drain. How long take empty the tank?
• Tourist Jirka
Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
• Two friends
Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and then replaced by Martin. Whole work was done in 6.5 hours. Calculate how long Peter worked before replaced by Martin.
• Diggers
The excavation was carried out in 4 days and 5 workers worked on it for 7 hours a day. Determine how long it would take to excavate if 7 workers worked on it 8 hours a day.
• James
James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether?
• Two companies
The family ordered two companies to modify the garden. The first would be done in 20 days, the second would take 40% less time. How long will they work together if the second company started working when the first worked for 4 days?
• Pond
A pond with two open floodgates will emptied in 20 days. A larger floodgate will emptied whole pond in 30 days. For how long would he be emptied with a smaller floodgate.
• Two workers
Two workers work together and perform the job in 12 hours. If one has done half the work and then second worker next half of work it will take 25 hours. How long would it take job them separately?