SOLUTION: Austin made the hike to Mt. St. Helen's in 4 hours, and Snelling made the same hike in 5 hours. How far was the hike if Austin hiked 1 mph faster than Snelling?

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Question 1206542: Austin made the hike to Mt. St. Helen's in 4 hours, and Snelling made the same hike in 5 hours. How far was the hike if Austin hiked 1 mph faster than Snelling?
Found 4 solutions by josgarithmetic, ikleyn, Edwin McCravy, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
PERSON            SPEED           TIME        DISTANCE
Austin            d%2F4                 4              d
Snelling          d%2F5                 5              d
Difference         1

Do you understand this and know what to do?



highlight%28d=20%29

Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
Austin made the hike to Mt. St. Helen's in 4 hours, and Snelling made the same hike in 5 hours.
How far was the hike if Austin hiked 1 mph faster than Snelling?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let d be the one way distance, in miles.

Then the rate by Austin   was  d%2F4  miles per hour,

     the rate by Snelling was  d%2F5  miles per hours.


We are given that Austin traveled 1 mph faster than Snelling,
so we can write this equation

    d%2F4 - d%2F5 = 1  mph.


At this point, the setup is complete.
To solve this equation, multiply both sides by 4*5 = 20, which is the common denominator.

You will get then

    5d - 4d = 20,

       d    = 20.


So, one way distance is 20 miles.    ANSWER

At this point, the solution is complete.



Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Austin made the hike to Mt. St. Helen's in 4 hours, and Snelling made the
same hike in 5 hours. How far was the hike if Austin hiked 1 mph faster than
Snelling?

All algebra books tell you make DRT tables for DRT problems:

          distance = rate * time
Austin   |    x    |  r+1 |  4
Snelling |    x    |   r  |  5


system%28x=4%28r%2B1%29%2C+x=5r%29

4%28r%2B1%29=5r
4r%2B4=5r
4=r

x = 5r = 5(4) = 20 miles

Edwin

Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


The formal algebraic solutions (or setups) shown by the other tutors are valid and useful.

But to learn how the problem can be solved informally almost immediately, you should be able to see that it makes sense that, because

(1) the distances are the same,
(2) the two times (4 hours and 5 hours) differ by 1 hour, and
(3) the two speeds differ by 1 mph

it must be that the two speeds are 5 mph and 4 mph.

So the distance is 4 hours at 5mph = 20 miles or 5 hours at 4mph = 20 miles.

ANSWER: 20 miles