Together, juanita and mark can make preparations to cater a dinner in 6 hours. alone, juanita can do the job 2 hours faster than mark. find the time that each person takes to prepare to cater a meal.

Time taken by Juanita and mark to cater meals is 11.08 hours or 11 hours 4 minutes and 13.08 hours or 13 hours 4 minutes respectively.

Solution:

Given, Together, Juanita and Mark can make preparations to cater a dinner in 6 hours.  

Alone, Juanita can do the job 2 hours faster than Mark.  

We need to find the time that each person takes to prepare to cater a meal.

Let the time taken by Juanita be x hours.

Then time taken by mark becomes x + 2 hours.

Now, work done by Juanita in 1 hour = [by assuming total work done as 1 unit]

And, work done by mark in 1 hour =

Together, in one hour they can complete  

work, which equals to

[ as given that together they completed in 6 hours ]

Now, by using quadratic formula,

We can neglect as time cannot be negative.

= 11.08 approximately

So, Juanita completes work alone in 11.08 hours or 11 hours 4 minutes approximately.

So, mark completes work in 11.08 + 2 = 13.08 hours or 13 hours 4 minutes approximately.

Hence, time taken by Juanita and mark to cater meals is 11.08 hours or 11 hours 4 minutes and 13.08 hours or 13 hours 4 minutes respectively.

faster, im not sure why but i know it is faster

the answer is d

hope this