The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.
Answer:
Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex] miles.
Step-by-step explanation:
Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3 [tex]\frac{2}{3}[/tex] miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.
To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.
The fraction can now be written as [tex]\frac{11}{3}[/tex]. The distance of Brookside trail to the end and back is
[tex]\frac{11}{3}[/tex] +
Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2 [tex]\frac{1}{2}[/tex] miles. We will add this distance twice as well to obtain the total distance traveled for this trail.
To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is [tex]\frac{5}{2}[/tex].
The distance of Forest Glen Trail to the end and back is:
[tex]\frac{5}{2}[/tex] +
The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.
[tex]\frac{22}{3}[/tex] + 5
This can be written as:
[tex]\frac{22}{3}[/tex] + [tex]\frac{5}{1}[/tex]
The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.
We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.
[tex]\frac{22}{3} + \frac{5 X 3}{1 X 3}[/tex]
= [tex]\frac{22}{3} + \frac{15}{3}[/tex]
= [tex]\frac{22+15}{3}[/tex]
= [tex]\frac{37}{3}[/tex]
To convert [tex]\frac{37}{3}[/tex] miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.
3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12 [tex]\frac{1}{3}[/tex]
Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex] miles.
