Question

Leon and Marisol biked the Brookside Trail to the end and back. Then they biked the Forest Glen Trail to the end and back before stopping to eat. How far did they bike before they stopped to eat?

Answer 1

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 $\frac{1}{3}$   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 $\frac{2}{3}$ 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 $\frac{11}{3}$. The distance of Brookside trail to the end and back is

$\frac{11}{3}$ +

Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2 $\frac{1}{2}$ 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 $\frac{5}{2}$.

The distance of Forest Glen Trail to the end and back is:

$\frac{5}{2}$ +

The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.

$\frac{22}{3}$ + 5

This can be written as:

$\frac{22}{3}$ + $\frac{5}{1}$

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.

$\frac{22}{3} + \frac{5 X 3}{1 X 3}$

= $\frac{22}{3} + \frac{15}{3}$

= $\frac{22+15}{3}$

= $\frac{37}{3}$

To convert $\frac{37}{3}$ 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 $\frac{1}{3}$

Before stopping to eat, Leon and Marisol biked a total distance of 12 $\frac{1}{3}$   miles.