SOLUTION: Practice Age word Problem Alfonso went to the internet cafe traveling 6 mph and returned home traveling 10 mph. If the total trip took 8 hours, how long did Alfonso travel at e

Algebra ->  Linear-equations -> SOLUTION: Practice Age word Problem Alfonso went to the internet cafe traveling 6 mph and returned home traveling 10 mph. If the total trip took 8 hours, how long did Alfonso travel at e      Log On


   

Question 1175281: Practice Age word Problem
Alfonso went to the internet cafe traveling 6 mph and returned home traveling 10 mph. If the total trip took 8 hours, how long did Alfonso travel at each speed?
Found 4 solutions by ewatrrr, josgarithmetic, ikleyn, greenestamps:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
D = rt  
  6mph*t = 10mph(8-t)     | Distance to and from the same
  16t = 80
    t = 5hrs at 6mph   and   3hr at 10mph

6mph*5hr = 10mph*3hr   30mi each way 
Wish You the Best in your Studies.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                   SPEEDS       TIMES     DISTANCE
Went To              6           8-x         d
Returned            10            x          d
TOTAL                             8


That is still, at those speeds, far to go to an internet cafe.
6%288-x%29=10x
-
3%288-x%29=5x
24-3x=5x
x=3

Went To, 5 hours
Returning Home, 3 hours

Thirty-Mile distance to the cafe.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Alfonso went to the internet cafe traveling 6 mph and returned home traveling 10 mph.
If the total trip took 8 hours, how long did Alfonso travel at each speed?
~~~~~~~~~~~~~~~


            There is another way to solve. 


Let d be the distance under the problem's question.


Then the time traveling to the cafe is  d%2F6  hours.

         time traveling back        is  d%2F10 hours.


Total time equation is


    d%2F6 + d%2F10 = 8  hours.


To solve it, multiply both sides by the common denominator of 30; then simplify


    5d + 3d = 8*30

      8d    = 8*30

       d    = 30 miles.      ANSWER

Solved.



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


And yet a very different (and fast and easy) way to solve the problem, if a formal algebraic solution is not required.

The ratio of the speeds is 6:10 = 3:5.
Since the distances both directions are the same, the times at the two speeds are in the ratio 5:3.
8 hours total divided in the ratio 5:3 means 5 hours one direction and 3 hours the other direction.
The distance is 5 hours times 6mph = 30 miles, or 3 hours times 10 mph = 30 miles.