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A man walked a certain distance at a constant rate. If he had gone 1/2​ mile per hour faster, he would have walked the distance in four-fifths the time; if he had gone 1/2​ mile per hour slower, he would have been 5/2​ hours longer on the road. How far did he walk?

 May 6, 2022
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Let total time taken==T

Let the distance walked==D

Let his original walking speed==S

 

4/5T + 5/2 ==T

T ==25 / 2 ==12.50 hours.

 

D / [S  +  1/2] ==4/5*(25/2),

D/ [S - 1/2] ==25 /2 + 5/2, solve for D, S

 

D==30 miles

S ==5/2 ==2.5 mph - his original speed

 May 6, 2022

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