SOLUTION: How far can a man walk into the country at the rate of 4mph if he rides back at the rate of 20 mph and his total time is 8 hours? Express your answer as a decimal number to the nea

Question 1163452: How far can a man walk into the country at the rate of 4mph if he rides back at the rate of 20 mph and his total time is 8 hours? Express your answer as a decimal number to the nearest hundredth.
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Let d be one way distance. Then you have this "time" equation + = 8 hours. The terms in the left side are the time intervals walking/riding in each direction. To solve the equation, multiply both sides by 20. You will get 5d + d = 8*20 6d = 160 d = 160/6 = 26 miles = 26.67 miles. ANSWER

Solved.

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On "time" equation, see the lesson
    - Time equation: HOW TO use, HOW TO write and HOW TO solve it
at this site.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
How far can a man walk into the country at the rate of 4mph if he rides back at the rate of 20 mph and his total time is 8 hours?
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His average speed is 2*4*20/(4+20) = 160/24 = 20/3 mi/hr
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The round trip distance = 8*(20/3)
Each way = 80/3 miles

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The distances out and back are the same; the ratio of speeds is 4:20 = 1:5.

That means the ratio of times at the two speeds is 5:1.

So 1/6 of the total time was spent returning.

1/6 of 8 hours is 8/6 hours, or 4/3 hours.

The distance traveled at 20mph in 4/3 hours is (4/3)*20 = 80/3 miles, or 26 2/3 miles.

ANSWER: 26 2/3 miles

Of course the same answer is obtained by finding how far he travels in 5/6 of the total time at the lower speed:

5/6 of 8 hours is 40/6 hours, or 20/3 hours.
20/3 hours at 4mph is (20/3)(4) = 80/3 miles.

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