SOLUTION: A worker drove to work traveling 65 miles per hour. He returned home traveling 55 miles per hour. What was his average speed if the entire trip took 4 hours?

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A worker drove to work traveling 65 miles per hour. He returned home traveling 55 miles per hour. What was his average speed if the entire trip took 4 hours?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 188738: A worker drove to work traveling 65 miles per hour. He returned home traveling 55 miles per hour. What was his average speed if the entire trip took 4 hours?
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A worker drove to work traveling 65 miles per hour. He returned home traveling 55 miles per hour. What was his average speed if the entire trip took 4 hours?
-----------------
d = rt
t = d/r
4 = d/55 + d/65
4 = (13d + 11d)/715
24d = 2860
d = 119 1/6 miles each way
r (avg) = 2d/4
r = 59 5/6 mph

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Alan made a slight error!
Edwin's solution:
A worker drove to work traveling 65 miles per hour. He returned home traveling 55 miles per hour. What was his average speed if the entire trip took 4 hours?

AVERAGE_SPEED+=+%28TOTAL_DISTANCE%29%2F%28TOTAL_TIME%29

Suppose the distance between his home and his word is N miles.

Then his total distance is 2N miles

Using TIME+=+DISTANCE%2FSPEED

His time going to work = N%2F65

His time returning home = N%2F55

Therefore his TOTAL_TIME+=+N%2F65%2BN%2F55

AVERAGE_SPEED+=+%28TOTAL_DISTANCE%29%2F%28TOTAL_TIME%29

AVERAGE_SPEED+=+%282N%29%2F%28N%2F65%2BN%2F55%29=%28%282N%29%2F1%29%2F%28N%2F65%2BN%2F55%29

The LCD is 715, so we multiply that fraction by 715%2F715
but we write it as %28715%2F1%29%2F%28715%2F1%29



AVERAGE_SPEED+=+%28%281430N%29%2F1%29%2F%28%28715N%29%2F65%2B%28715N%29%2F55%29

AVERAGE_SPEED+=+%281430N%29%2F%2811N%2B13N%29

AVERAGE_SPEED+=+%281430N%29%2F%2824N%29

AVERAGE_SPEED+=+%281430cross%28N%29%29%2F%2824cross%28N%29%29

AVERAGE_SPEED+=+1430%2F24

AVERAGE_SPEED+=+715%2F12

AVERAGE_SPEED+=+59%267%2F12 miles per hour

Notice three things here:

1.  We did not even use the 4 hours!
2.  The distance N miles between his home and work
    canceled out.

This means that the time and the distance are independent
of the average speed.

3.  Important!  To find the average speed, it does not 
    work to just average the two speeds! For that would 
    have been 60 mph not 59%267%2F12mph.

Edwin