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?

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Answer 1 · 2017-07-13T21:25:05

From #4 5/8# feet behind,to #3 2/3# feet ahead

is a change of # 8 7/8# feet

There are two parts to be considered:

A distance of #4 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 2/3#

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

#4 5/8 + 3 2/3#

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

#= 7 (15 +16)/24" "larr# find equivalent fractions

#= 7 31/24 = 7+ 1 7/8#

#= 8 7/8#

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

#3 2/3 - (-4 5/8)#

#=3 2/3 + 4 5/8#

Which will produce the same result as shown above.