SOLUTION: Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home on the interstate at 60mi/hr. The total trip took 6 hours. How far is Mr. Thomas's home from the

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home on the interstate at 60mi/hr. The total trip took 6 hours. How far is Mr. Thomas's home from the      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1188476: Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home on the interstate at 60mi/hr. The total trip took 6 hours. How far is Mr. Thomas's home from the city
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home
on the interstate at 60mi/hr. The total trip took 6 hours.
How far is Mr. Thomas's home from the city
~~~~~~~~~~~~~~ 

Let d be one way distance (which is the unknown value under the problem's question).


Write the total time equation


    d%2F40 + d%2F60 = 6  hours.


To solve it, multiply both sides by 120.  You will get


    3d + 2d = 6*120

      5d    = 720

       d    = 720/5 = 144 miles.


ANSWER.  The distance is 144 miles.

Solved (and corrected).



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Mr. Thimas drove his old truck to the city at a rate of 40mi/hr and drove back home on the interstate at 60mi/hr. The total trip took 6 hours. How far is Mr. Thomas's home from the city
------------------
Avg speed = 2*40*60/(40+60) = 48 mi/hr
6*48 = 288 miles RT, 144 miles each way

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The first tutor used a standard formal algebraic solution method but used the wrong total travel time; I'm sure she will see this note and fix her response.

The second tutor used a magic formula which is well worth remembering, since it appears in a large number of similar problems:

The average speed for traveling from A to B and back at speeds of x and y is

%282xy%29%2F%28x%2By%29

Here is another informal way to solve the problem quickly, if formal algebra is not required.

The ratio of the two speeds is 40:60 = 2:3, and the distances are the same, so the ratio of times at the two speeds is 3:2.

So 3/5 of the total travel time of 6 hours was at 40mph, and 2/5 was at 60mph. Using either of those facts gives the distance:

3/5 of 6 hours at 40mph: (3/5)(6)(40) = 144 miles
2/5 of 6 hours at 60mph: (2/5)(6)(60) = 144 miles