Question

Phil and Meredith work for a book publisher editing mathematics textbooks. Phil has less experience and takes twice​ as long as Meredith to edit a textbook. Together, it takes them 6 hours to edit a textbook.

How long does it take Phil to edit a textbook if he works alone?
_ hours.

How long does it take Meredith to edit a textbook if she works alone?
_ hours

Answer 1

• Phil = 18 hours
• Meredith = 9 hours

Explanation:

Let's take for a hour,

→ Phil = 1/2t

→ Meredith = 1/t

Forming the equation,

→ (1/2t) + (1/t) = 1/6

Now the value of time (t) will be,

→ (1/2t) + (1/t) = 1/6

→ (1/2t) + (2/2t) = 1/6

→ 3/2t = 1/6

→ 2t/3 = 6

→ 2t = 6 × 3

→ t = 18/2

→ [ t = 9 ]

Then time for each person is,

→ Phil = 2t = 2(9) = 18 hours

→ Meredith = t = 9 hours

Hence, these are the time taken.

Answer 2

Let the time for Meredith to finish the work alone be x, then for Phil it is 2x.

In one hour Meredith edits 1/x and Phil edits 1/(2x) of the text.

Set equation for the work together

• 1/x + 1/(2x) = 1/6
• (2 + 1)/(2x) = 1/6
• 2x = 3*6
• 2x = 18
• x = 9

• Meredith - 9 hours,
• Phil - 18 hours.