Question

Horatio spends about 40 hours per week reading 2 different books in his spare

time. One book is more difficult, and one is lighter. He reads about 12 pages per
hour of the more difficult book and 25 pages per hour of the lighter book. If he
reads 610 pages per week, how many hours does Horatio spend on each book?

Answer 1

you add 40+12+25+2+610 and you will get your answer

Answer 2

Horatio spends 30 hours on the more difficult book and 10 hours on the lighter book

Explanation:

Let X be the hours spent reading the more difficult book
Let Y be the hours spent reading the less difficult book

Total hours spent = X + Y = 40

Number of pages of difficult book in X hours at 12 pages per hour = 12X

Number of pages of easier book in Y hours at 25 pages per hour = 25Y

Total pages read = 12X + 25Y

So we have two equations in X and Y and we can solve them simultaneously. Equations are:

X + Y = 40 (1)

12X + 25Y = 610 (2)

We can eliminate one of the variable terms by making the coefficients of the other term equal and then subtracting

Multiply (1) by 12 to make X terms equal
12(X + Y) = 12 x 40
12X + 12Y = 480 (3)

Subtract (3) from (2)

(2) - (3)

==> 12X + 25Y - (12X + 12Y) = 610 - 480

==> 12X + 25Y - 12X - 12Y = 130

==> 25Y - 12Y = 130 (12X terms cancel)

==> 13Y = 130

==> Y = 130/13 (divide both sides by 13)

==> Y = 10

Using (1)
X + Y = 40

==> X + 10 = 40
==> X + 10 - 10 = 40 - 10

==> X = 30

So answer:
Horatio spends 30 hours on the more difficult book and 10 hours on the lighter book