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?

Result

t =  11.9 min

Solution:

95t5+5t=1 4t+5(t5)=t(t5)  t214t+25=0  a=1;b=14;c=25 D=b24ac=1424125=96 D>0  t1,2=b±D2a=14±962=14±462 t1,2=7±4.89897948557 t1=11.8989794856 t2=2.10102051443   Factored form of the equation:  (t11.8989794856)(t2.10102051443)=0  t>5 t=11.9 min\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}

Checkout calculation with our calculator of quadratic equations.




Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




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?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  1. 2 pipes
    time_12 2 pipes can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less time than the smaller pipe. How long does each pipie take to fill the tank alone?
  2. Two masons
    garage 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?
  3. Work
    workers_21 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
  4. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  5. Hectoliters of water
    pumps_7 The pool has a total of 126 hectoliters of water. The first pump draws 2.1 liters of water per second. A second pump pumps 3.5 liters of water per second. How long will it take both pumps to drain four-fifths of the water at the same time?
  6. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  7. Seven
    trpaslíky Seven dwarfs will cut 420 stumps in 15 hours. After five hours, the two dwarves disappear discreetly. How many hours will the remaining dwarves complete the task?
  8. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  9. Three people
    clocks_16 Three people start doing a work at a same time. The first worked only 2 hours. The second ended 3 hours before the end. On an individual basis, it would take the first time to do the work 10 hours, second 12 hours and 15 hours third. How many hours did it
  10. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  11. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  12. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  13. Novak
    novakovci Novak needed to dig up three of the same pit in the garden. The first pit dug father alone for 15 hours. His second dig son helped him and it did that in six hours. The third pit dug son himself. How long it took him?
  14. The product
    eq222 The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
  15. Two pipes
    2pipes One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately?
  16. Wind drift
    airplane The plane flies at 860 km/h, passing distance 3000 kilometers with the wind and once again against the wind for 6 h 59 min. What is the wind speed?
  17. Invitations
    envelope For every 5 minutes writes Dana 10 invitations, while Anna 14 invitations. How long will write together 120 invitations?