Question

Working by herself, Mary requires 16 minutes more than Antoine to solve a mathematics problem. Working together, Mary and Antoine can solve a problem in 6 minutes. If this situation is represented by the equation (6/t)+(6/t+16)=1 , where t represents the number of minutes Antoine works alone to solve the problem, how many minutes will it take Antoine to solve the problem if he works by himself?

Answer 1

Explanation:

Given

Mary requires
`16` minutes more than Antoine

If Antoine requires
`t` minutes

so time required by Mary is
`16+t`

in 1 one minute Antoine do
`(1)/(t)` minute

Mary does
`(1)/(16+t)`

Total work done in 6 minutes

`(6)/(t)+(6)/(16+t)=1`

`(t+16+t)/((16+t)t)=(1)/(6)`

`12t+96=t^2+16t`

`t^2+4t-96=0`

`(t+12)(t-8)=0`

thus
`t=8 min`

Antoine requires 8 minute to complete the work by himself