# Before a race, you start 4 5/8 feet behind your friend. At the halfway point you are 3 2/3 feet ahead of your friend. What is the change in distance between you and your friend from the beginning of the race?

Jul 13, 2017

From $4 \frac{5}{8}$ feet behind,to $3 \frac{2}{3}$ feet ahead

is a change of $8 \frac{7}{8}$ feet

#### Explanation:

There are two parts to be considered:

A distance of $4 \frac{5}{8}$ needs to be gained so that you are running next to your friend, then you pull away in front of him by a distance of $3 \frac{2}{3}$

Therefore, the change in distance is the sum of these distances:

$4 \frac{5}{8} + 3 \frac{2}{3}$

= 7 (color(white)(???????))/24" "larr find the common denominator

$= 7 \frac{15 + 16}{24} \text{ } \leftarrow$ find equivalent fractions

$= 7 \frac{31}{24} = 7 + 1 \frac{7}{8}$

$= 8 \frac{7}{8}$

You could also regard the distance behind the friend as being negative and then subtract to find the difference:

$3 \frac{2}{3} - \left(- 4 \frac{5}{8}\right)$

$= 3 \frac{2}{3} + 4 \frac{5}{8}$

Which will produce the same result as shown above.