Question

megan spent the weekend hiking with friends. the group hiked for $2\frac{2}{3}$ hours on saturday morning and $3\frac{3}{4}$ hours that afternoon. on sunday, they hiked for $2\frac{1}{3}$ hours in the morning and $1\frac{3}{4}$ hours in the afternoon. how much more time did the group spend hiking on saturday than on sunday?

Explanation:

Step1: Calculate Saturday's total hiking time

First, add the morning and afternoon hiking times on Saturday. The morning time is \(2\frac{2}{3}\) hours and the afternoon time is \(3\frac{3}{4}\) hours. Convert the mixed numbers to improper fractions: \(2\frac{2}{3}=\frac{8}{3}\) and \(3\frac{3}{4}=\frac{15}{4}\). Find a common denominator, which is 12. So \(\frac{8}{3}=\frac{32}{12}\) and \(\frac{15}{4}=\frac{45}{12}\). Add them: \(\frac{32}{12}+\frac{45}{12}=\frac{77}{12}=6\frac{5}{12}\) hours.

Step2: Calculate Sunday's total hiking time

Add the morning and afternoon hiking times on Sunday. The morning time is \(2\frac{1}{4}\) hours and the afternoon time is \(1\frac{3}{4}\) hours. Convert to improper fractions: \(2\frac{1}{4}=\frac{9}{4}\) and \(1\frac{3}{4}=\frac{7}{4}\). Add them: \(\frac{9}{4}+\frac{7}{4}=\frac{16}{4}=4\) hours.

Step3: Find the difference between Saturday and Sunday times

Subtract Sunday's total from Saturday's total: \(6\frac{5}{12}-4 = 2\frac{5}{12}\) hours.

Answer:

\(2\frac{5}{12}\)