SOLUTION: Michael averaged running a certain distance 1 mph faster than David ran the same distance. If it took Michael 36 minutes to run the distance and it took David 4 minutes longer to r

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Question 1048956: Michael averaged running a certain distance 1 mph faster than David ran the same distance. If it took Michael 36 minutes to run the distance and it took David 4 minutes longer to run the same distance, how far did the boys run?
I don't even know how to begin to set up this problem into an equation, other than distance=rateXtime.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
According to RT=D for the basic constant travel rates rule, here is an the tabulation for the problem description. 

Speed unit of MILES per HOUR, time unit as HOURS, and distance as MILES:

               SPEED             TIME               DISTANCE
Michael        r+1               36/60               d
David           r                4/60+36/60          d

If you understand that, then simplify the time values. 

Speed unit of MILES per HOUR, time unit as HOURS, and distance as MILES:

               SPEED             TIME             DISTANCE

Michael        r+1                              d

David           r                               d

Next is formulate two equations and solve.
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Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Michael averaged running a certain distance 1 mph faster than David ran the same distance. If it took Michael 36 minutes to run the distance and it took David 4 minutes longer to run the same distance, how far did the boys run?
I don't even know how to begin to set up this problem into an equation, other than distance=rateXtime. 
Let distance be D

Then Michael’s speed = , or , or , or 

David’s speed = , or , or , or , or 

We then get: 

10D = 9D + 6 ------- Multiplying by LCD, 6

10D – 9D = 6

D, or distance = 



Nothing complex....it's that easy! You want DISTANCE, so solve for nothing else but DISTANCE! 

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