SOLUTION: Sally walked to the store from her home at the rate of 5 miles per hour. After spending one-half hour in the store, her friend gave her a ride home at the rate of 30 miles per hour

Algebra ->  Finance -> SOLUTION: Sally walked to the store from her home at the rate of 5 miles per hour. After spending one-half hour in the store, her friend gave her a ride home at the rate of 30 miles per hour      Log On


   

Question 1162990: Sally walked to the store from her home at the rate of 5 miles per hour. After spending one-half hour in the store, her friend gave her a ride home at the rate of 30 miles per hour. She arrived home 1 hour and 5 minutes (1 1/12 hours) after she left from home. How far is the store from Sally’s home?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let d be the distance from home to the store, in miles (one way distance).


The total time traveling both ways is  11%2F12 hours - 1%2F2 of an hour = 13%2F12+-+6%2F12 = 7%2F12 of an hour.


Time walking  is  d%2F5  hours.

Time riding back is  d%2F30  hours.


Total time equation is


    d%2F5 + d%2F30 = 7%2F12   of an hour.


To solve it, multiply both sides by 60.  You will get


    12d  +  2d  = 35,

    14d         = 35

      d         = 35%2F14 = 2.5  miles.    ANSWER

Solved.

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

Using  "time"  equation is a  STANDARD  method of solving such problems.
From my post,  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(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative method for solving a problem like this, if a formal algebraic solution is not required.

For me, this alternative method is much faster than using formal algebra to write and solve an equation.

The time spent driving is the total time of 1 1/12 hours, minus the 1/2 hour she spent in the store; that is 7/12 of an hour.

The ratio of the walking and riding speeds is 1:6; so the amounts of time walking and riding are in the ratio 6:1.

That means 6/7 of the total travel time was walking and 1/7 of it was riding. That means 6/12 = 1/2 hour walking and 1/12 hour riding.

The distance to the store is (1/2 hour)*(5mph) = 2.5 miles.
or...
The distance to the store is (1/12 hour)*(30mph) = 2.5 miles.