SOLUTION: How far can a man drive into a country if he drives out at 40 miles per hour, returns over the same road at 30 miles per hour, and spends 8 hours away from home, including a 1-hour

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Question 995930: How far can a man drive into a country if he drives out at 40 miles per hour, returns over the same road at 30 miles per hour, and spends 8 hours away from home, including a 1-hour stop for lunch?
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Eight hours away from home and 1 hour for lunch means total time traveling, 7 hours.

Let variables' meaning be implied in this table.
                speed    time    distance
TO COUNTRY      40        c      40c
TO HOME         30        h      30h
Total                     7                         

This does not help.



Distance each way should be the same, some number d.

 
               speed   time       distance
TO COUNTRY      40      d/40       d
TO HOME         30      d/30       d
Total                   7



This is more useful.

-



Solve for d. 

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
 How far can a man drive into a country if he drives out at 40 miles per hour, returns over the same road at 30 miles per hour, and spends 8 hours away from home, including a 1-hour stop for lunch?

--------------

Avg speed of a round trip = 2*r1*r2/(r1 + r2)

= 2*40*30/(40+30) = 240/7 mi/hr

Driving for 7 hours --> RT distance = (240/7)*7 = 240 miles

--> 120 miles each way. 

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