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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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      Log On

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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(52832) About Me  (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   120%2F5 = 24 hours.

Mike spends   60%2F6 + 60%2F4 = 10 + 15 = 25 hours.

Jake is faster.

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    For the general case, if D is the distance, then Jake spends  D%2F5  hours.   (1)


    Mike spends  %28%28D%2F2%29%29%2F6 + %28%28D%2F2%29%29%2F4 = D%2F12+%2B+D%2F8 = %288%2AD+%2B+12%2AD%29%2F48 = %2820%2AD%29%2F96 = D%2F%28%2896%2F20%29%29  hours.    (2)


    In (2),  the denominator   96%2F20   is LESS THAN 5,  so the fraction  (2)  is GREATER  than fraction (1),

    which means, again, that Mike is slower.


Answer by josgarithmetic(39623) About Me  (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?
d%2F%28d%281%2F12%2B1%2F8%29%29

1%2F%281%2F12%2B1%2F8%29

1%2F%282%2F24%2B3%2F24%29

1%2F%285%2F24%29

24%2F5

This is highlight%284%264%2F5%29 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.