SOLUTION: You and your roommate decided to take a road trip to the beach one weekend. You drove all the way to the beach at an average speed of 60 miles per hour. Your roommate drove all th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You and your roommate decided to take a road trip to the beach one weekend. You drove all the way to the beach at an average speed of 60 miles per hour. Your roommate drove all th      Log On


   

Question 1195933: You and your roommate decided to take a road trip to the beach one weekend. You drove all the
way to the beach at an average speed of 60 miles per hour. Your roommate drove all the way back
(on the same route, but with no traffic) at an average rate of 75 miles per hour. If the round trip
drive took a total of 9 hours, how many miles was the trip to the beach?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
You and your roommate decided to take a road trip to the beach one weekend.
You drove all the way to the beach at an average speed of 60 miles per hour.
Your roommate drove all the way back (on the same route, but with no traffic)
at an average rate of 75 miles per hour. If the round trip
drive took a total of 9 hours, how many miles was the trip to the beach?
~~~~~~~~~~~~~~ 

Let d be the one way distance, in miles.


Then the trip to the beach takes  d%2F60  hours,
while the trip back takes  d%2F75  hours.


The total time equation is

    d%2F60 + d%2F75 = 9  hours.


To solve it, multiply both sides by 300.  You will get then

    5d + 4d = 9*300

      9d    = 9*300

       d    = 300 miles.


ANSWER.  The trip to the beach is 300 miles long.


CHECK. 300%2F60 + 300%2F75 = 5 + 4 = 9 hours, total travel time.     ! Correct !

Solved.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                  SPEED             TIME           DISTANCE

GOING TO            60               d/60              d

RETURNING           75               d/75              d

TOTAL                                 9

highlight_green%28d%2F60%2Bd%2F75=9%29

The denominators are 2%2A2%2A3%2A5 and 3%2A5%2A5.
Common denominator could be 2%2A2%2A3%2A5%2A5.

%28d%2F60%29%285%2F5%29%2B%28d%2F75%29%28%282%2A2%29%2F%282%2A2%29%29=9
%285d%29%2F300%2B%284d%29%2F300=9
9d%2F300=9
d=9%28300%2F9%29
highlight%28d=300%29

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


Both responses from other tutors show a typical formal algebraic solution using the time equation "time going plus time returning equals 9 hours".

Here is a very different way to solve problems like this quickly and easily when the numbers are "nice".

The distances both directions are of course the same; the ratio of speeds is 60:75 = 4:5; that means the ratio of times at the two speeds is 5:4.

Since the total time was 9 hours, the trip to the beach took 5 hours and the trip back took 4 hours.

The distance to the beach was either 5 hours at 60mph equals 300 miles or 4 hours at 75mph equals 300 miles.

ANSWER: 300 miles