SOLUTION: Jake and Mike are running from point A to point B. Jake runs at a rate of 5 mph the whole way. Mike runs half the distance at 6 mph, then runs the rest at 4 mph. Which one reaches

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Question 1107449: Jake and Mike are running from point A to point B. Jake runs at a rate of 5 mph the whole way. Mike runs half the distance at 6 mph, then runs the rest at 4 mph. Which one reaches point B first? Explain
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52919)   (Show Source): You can put this solution on YOUR website!
.
To make the solution highly visible, assume that the whole distance is  120 miles.

Then Jake spends    = 24 hours.

Mike spends    + = 10 + 15 = 25 hours.

Jake is faster.

------------------
    For the general case, if D is the distance, then Jake spends    hours.   (1)


    Mike spends   +  =  =  =  =   hours.    (2)


    In (2),  the denominator      is LESS THAN 5,  so the fraction  (2)  is GREATER  than fraction (1),

    which means, again, that Mike is slower.


Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Look for average speed for Mike.
firstpart        6     d/12       d/2
secondpart       4     d/8        d/2
total                d(1/12+1/8)   d

What is average speed of Mike?










This is mph for Mike.

Now, Same distance for Jake and Mike;
Jake went 5 mph, and Mike went 4&4/5 mph.
JAKE went this given but unstated distance FASTER, so JAKE reached point B first.
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