Question 1163952: 2 people walk towards each other on a road. It takes the first person 2 hours to walk the road, it takes the 2nd person 3 hours to walk the road. When they meet, the first person walked 4 and 4/5 of a mile more than the 2nd person. How long is the road?
Found 2 solutions by htmentor, ikleyn:
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The first person's speed is s1 = d/2 (mi/h) where d is the total length of the road
The second person's speed is s2 = d/3 (mi/h)
The first person has walked a distance of d/2 + 4 4/5 when they meet
The second person has walked a distance of d/2 - 4 4/5 when they meet
Since they both walk for the same time, we can set the times equal to each other:
time = distance/speed
(d/2 + 4 4/5)/(d/2) = (d/2 - 4 4/5)/(d/3)
Solve for d: d + 48/5 = 3d/2 - 72/5
d/2 = 120/5 -> d = 48 mi
Answer by ikleyn(52775)  (Show Source):
You can put this solution on YOUR website! .
Two persons walk towards each other on a road. It takes the first person 2 hours to walk the road, it takes the 2nd person 3 hours to walk the road.
When they meet, the first person walked 4 and 4/5 of a mile more than the 2nd person. How long is the road?
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Since their times to cover the entire distance are in the ratio  =  , it means that their rates are in reciprocal ratio  =  .
In turn, it means that going toward each other, they cover the distances, whose ratio is the same as the ratio of their speeds, i.e. .
So, if "d" is the total one way distance, then the first person covered  of the distance, while the second covered  of the distance.
Then from the condition, you have this equation
 -  =   miles, or
 =  miles,
d = 24 miles. ANSWER
Solved.
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Notice that the solution by the tutor @htmentor is incorrect, since he incorrectly interprets the condition.
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