Question

A new computer can complete a complex biochemistry calculation in 11 hours less than an older-model computer. Working together, the new computer and the old computer can complete the calculation in 19 hours. How long would it take the new computer to complete the calculation by itself

Answer 1

New computer will take 33.28 hours to complete the calculation by itself.

Explanation:

Let the time taken by the new computer to complete the calculation = x hours

Per hours work done by the new computer =
`(1)/(x)`

Time taken by the older computer to complete the calculation = (x + 11) hour

Per hour work done by old computer =
`(1)/((x+11))`

When both the computers work together they complete the work in 19 hours.

Therefore, per hour work done by both together =
`(1)/(19)`

We per hour work done by both individually = per hour work done by both together

`(1)/(x)+(1)/(x+11)=(1)/(19)`

`(x+x+11)/(x(x+11))=(1)/(19)`

`(2x+11)/(x(x+11))=(1)/(19)`

38x + 209 = x² + 11x

x² - 27x - 209 = 0

By quadratic formula,

x =
`\frac{27\pm \sqrt{(-27)^(2)-4* 1* (-209)}}{2}`

x =
`(27\pm √(729+836))/(2)`

x =
`(27\pm √(1565))/(2)`

x =
`(27\pm 39.56)/(2)`

x = 33.28 hours

Therefore, new computer will take 33.28 hours to complete the calculation by itself.