A man walked half of the total distance in the morning. After lunch, he walked 1/2 of the remaining distance. In late afternoon he walked half the distance that was left.  After dinner he walked the last 3 miles. How far did he walk altogether?

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## 1 Answer

There are 4 seperate walks here which add up to the total distance. Set each to a variable

total distace = t

morning = m

after lunch = l

afternoon = a

after dinner = d

your equation then is t=m+l+a+d

we know that d = 3 miles

If the man walks half the total distance in the morning

m=1/2t

If he walks half of the remaining distance after lunch

l=(1/2)1/2t or 1/4t

If he walks 1/2 the remaining distace in the afternoon

a=(1/2)1/4t or 1/8t

and we know that the final distance is 3 miles

Now we can plug in the values for all of the variables since we have only t left

m+l+a+d=t

1/2t+1/4t+1/8t+3=t

combine all the t terms on the left

7/8t+3=t

subtract 7/8t from both sides

3=1/8t

multiply both sides by 1/8

t=24 miles

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