Question

for a read-a-thon, jay and odhràn each started reading a book at the same time and continued reading for several hours. jays book had 278 pages, and he read 55 pages per hour. odhràns book had 238 pages, and he read 45 pages per hour. after how many hours did they have the same number of pages left, and how many pages were left? after \square hours, both boys had \square pages left.

Explanation:

Step1: Define variables and equations

Let \( h \) be the number of hours they read. The number of pages left for Jay is \( 278 - 55h \), and for Odhràn is \( 238 - 45h \). We set them equal: \( 278 - 55h = 238 - 45h \).

Step2: Solve for \( h \)

Subtract \( 238 \) from both sides: \( 40 - 55h = -45h \). Add \( 55h \) to both sides: \( 40 = 10h \). Divide by \( 10 \): \( h = 4 \).

Step3: Find pages left

Substitute \( h = 4 \) into Jay's equation: \( 278 - 55(4) = 278 - 220 = 58 \). Check with Odhràn's: \( 238 - 45(4) = 238 - 180 = 58 \).

Answer:

After \( \boldsymbol{4} \) hours, both boys had \( \boldsymbol{58} \) pages left.