SOLUTION: What is Alicia's average speed on her walk to school if she walks halfway at 2 mph and runs the rest of the way at 7 mph?

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Question 1207696: What is Alicia's average speed on her walk to school if she walks halfway at 2 mph and runs the rest of the
way at 7 mph?
Found 4 solutions by ikleyn, josgarithmetic, Edwin McCravy, greenestamps:
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.
What is Alicia's average speed on her walk to school if she walks
halfway at 2 mph and runs the rest of the way at 7 mph?
~~~~~~~~~~~~~~~~~~~ 

This problem is very special.


In this problem, we have two halves of the entire way,
and the halves are, of course, of equal length.


For this specific situation, the simplest way to find the average speed is to use well known formula


   average speed = %282uv%29%2F%28u%2Bv%29 = %282%2A2%2A7%29%2F%282%2B7%29 = 28%2F9 = 31%2F9 = 3.111111111... miles per hour.   ANSWER

Solved.

This formula is specially derived and works only for the case,
when two parts of the traveled distance have equal lengths.

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

There are other ways to solve this problem.


About these other ways,  see the lessons
    - Calculating an average speed: a train going from A to B and back
    - One more problem on calculating an average speed
in this site.     Learn the entire subject from there.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
SPEED%2ATIME=DISTANCE
Not given the distances exactly 
                  SPEED    TIME            DISTANCES

FIRST HALF          2        d/4              d/2

LAST HALF           7        d/14             d/2

FULL                      d/4+d/14            d

Basic Rule means SPEED=DISTANCE%2FTIME.

d%2F%28d%2F4%2Bd%2F14%29, easily simpliable.

1%2F%281%2F4%2B1%2F14%29

%2828%2F28%29%281%2F%281%2F4%2B1%2F14%29%29
28%2F%287%2B2%29
28%2F9

highlight%283%261%2F9%29

(check for possible mistakes.)

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let's pick a ridiculous distance to school, one that halfway is divisible
by both 2 and 7.  Halfway would be 14 miles and the whole distance to school
would be 28 miles.

(Yes, I know that's a long way to walk and run to school! lol). Anyway,

She walks the first 14 miles at 2 mph, which takes her 7 hours.

She runs the remaining 14 miles at 7 mph in 2 hours.

So she travels 28 miles in 9 hours.

So her average speed is 28/9 = 3 1/9 mph.

Edwin

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


She travels equal distances at the two speeds of 2mph and 7mph.

Since the ratio of speeds is 2:7 and the distances are the same, the ratio of times spent at the two speeds is 7:2.

We can calculate her average speed as a weighted average -- she spends 7/9 of her time at 2mph and 2/9 of her time at 7mph; her average speed is

(7/9)*2+(2/9)*7 = 14/9+14/9 = 28/9

ANSWER: 28/9 mph, or 3 1/9 mph