SOLUTION: A family goes on vacation to a water park. During the drive to the water park the weather caused the family to average 44 miles per hours. After their vacation the weather improved

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Question 1144165: A family goes on vacation to a water park. During the drive to the water park the weather caused the family to average 44 miles per hours. After their vacation the weather improved, so they could average 80 miles per hour on the return trip. If the distance each way was equal, and the entire time driving was 6.2 hours, find the distance one way to the water park.
Found 4 solutions by josgarithmetic, ikleyn, greenestamps, Alan3354:
Answer by josgarithmetic(39616) About Me  (Show Source):
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During the drive to the water park the weather caused the family to average 44 miles per hours. After their vacation the weather improved, so they could average 80 miles per hour on the return trip. If the distance each way was equal, and the entire time driving was 6.2 hours, find the distance one way to the water park.
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During the drive to the water park the weather caused the family to average G miles per hours. After their vacation the weather improved, so they could average R miles per hour on the return trip. If the distance each way was equal, and the entire time driving was T hours, find the distance one way to the water park.
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                 SPEED         TIME        DISTANCE

GOING               G           d/G          d

RETURNING           R           d/R          d

TOTAL                            T

highlight_green%28d%2FG%2Bd%2FR=T%29

Rd%2BGd=RGT
d%28R%2BG%29=RGT
highlight%28d=RGT%2F%28R%2BG%29%29
.
.

Answer by ikleyn(52775) About Me  (Show Source):
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Let d be the distance under the question, in miles.


Then the time moving  TO        the water park was  d%2F44  hours.

     The time moving  BACK from the water park was  d%2F80  hours.


The total time was 6.2 hours, which gives you this "time" equation


    d%2F44 + d%2F80 = 6.2  hours.


To solve it, multiply both sides by 880. You will get


     20d + 11d = 6.2*880,

     31d       = 62*88

       d       = %2862%2A88%29%2F31 = 2*88 = 176 miles.    ANSWER


CHECK.   176%2F44 + 176%2F80 = 4 + 2.2 = 6.2 hours.    ! Correct !

Solved.

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Using  "time"  equation is the  STANDARD  method of solving such problems.
From this lesson,  learn on how to write,  how to use and how to solve a  "time"  equation.

To see many other similar solved problems,  look into the lessons
    - Had a car move faster it would arrive sooner
    - How far do you live from school?
    - Earthquake waves
    - Time equation: HOW TO use, HOW TO write and HOW TO solve it
in this site.


Answer by greenestamps(13198) About Me  (Show Source):
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The ratio of the two speeds is 80:44 = 20:11, and the distances are the same; therefore, the ratio of the times spent at the two speeds is 11:20. So

let 11x = time spent at 80mph
let 20x = time spent at 44mph

The total driving time was 6.2 hours:

11x%2B20x+=+6.2
31x+=+6.2
x+=+0.2

The driving time at 80mph was 11x = 2.2 hours, so the distance was 80*2.2 = 176 miles.

or...

The driving time at 44mph was 20x = 4 hours, so the distance was 44*4 = 176 miles.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A family goes on vacation to a water park. During the drive to the water park the weather caused the family to average 44 miles per hours. After their vacation the weather improved, so they could average 80 miles per hour on the return trip. If the distance each way was equal, and the entire time driving was 6.2 hours, find the distance one way to the water park.
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The avg speed of the round trip is 2*44*80/(44+80)
= 7040/124 = 1760/31 mi/hr
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d of the RT = (1760/31)*6.2 = 352 miles
---> 176 miles one way
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