Question

Grayson and Claire are reading the same book. At the beginning of the month,Grayson was on page 40 and Claire was on page 19. Grayson will read 7 pages per dayand Claire will read 14 pages per day. Let G represent the page of the book thatGrayson is on at the end of t days into the month, and let C represent the page of thebook that Claire is on at the end of t days into the month. Write an equation for eachsituation, in terms of t, and determine after how many days, t, Grayson and Clairewill be on the same page of the book.

Answer 1

G represent the page of the book that Grayson is on at the end of t days

C represents the page of the book that Claire is on at the end of t days

So, at the beginning of the month;

Grayson was on page 40

Claire was on page 19

During the month :

Grayson will read 7 pages per day

Claire will read 14 pages per day

When t represents the number of days, So:

G = 40 + 7 t

C = 19 + 14 t

When Grayson and Claire will be on the same page, G will be equal to C

So,

G = C

So,

40 + 7t = 19 + 14 t

Solve to find t

Combine like terms

-14 t + 7t = 19 - 40

-7 t = -21

Divide both sides by -7

t = -21/-7 = 3

So, after 3 days they will be on the same page of the book.