SOLUTION: A truck traveled at an average speed of 60 miles per hour on a 200 mile trip to pick up a load of freight. On the return trip, with the truck fully loaded, the average speed was 40

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A truck traveled at an average speed of 60 miles per hour on a 200 mile trip to pick up a load of freight. On the return trip, with the truck fully loaded, the average speed was 40      Log On


   

Question 88456: A truck traveled at an average speed of 60 miles per hour on a 200 mile trip to pick up a load of freight. On the return trip, with the truck fully loaded, the average speed was 40 miles per hour.
My teacher want the class to use the formula for speed distance and time but it is not in my textbook and I got confused looking on the internet. I need the formula to figure out the average speed for the round trip. Thanks.
Found 2 solutions by Earlsdon, Edwin McCravy:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's find the time taken by the truck on each leg of the trip:
The required formulas are:
t%5B1%5D+=+d%5B1%5D%2Fr%5B1%5D for the outbound trip, and:
t%5B2%5D+=+d%5B2%5D%2Fr%5B2%5D for the return trip.
Where: d = distance, r = rate(speed), and t = time of trip.
So:
t%5B1%5D+=+200%2F60
t%5B1%5D+=+10%2F3hrs.
t%5B2%5D+=+200%2F40
t%5B2%5D+=+5hrs.
Since you already know the average speed for the outbound trip (60 mph) and the return trip (40 mph), you may think that the average speed for the round trip would be:%2860%2B40%29%2F2+=+50mph.
However, the truck did not travel these speeds for equal amounts of time, so you have to find the weighted average, M, for the trip. This is given by:
M+=+%28d%5B1%5D%2Bd%5B2%5D%29%2F%28t%5B1%5D%2Bt%5B2%5D%29
M+=+%28200%2B200%29%2F%28%2810%2F3%29%2B5%29 Simplifying this, you get:
M+=+%28400%29%2F%28%2825%2F3%29%29 Invert the denominator and multiply.
M+=+%28400%29%283%2F25%29
M+=+48mph.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A truck traveled at an average speed of 60 miles per hour on a 200 mile trip to pick up a load of freight. On the return trip, with the truck fully loaded, the average speed was 40 miles per hour.
My teacher want the class to use the formula for speed distance and time but it is not in my textbook and I got confused looking on the internet. I need the formula to figure out the average speed for the round trip. Thanks.


There are three equivalent equations, and we use whichever one we need:

D+=+RT which means DISTANCE+=+RATE%2ATIME

R+=+D%2FT which means RATE+=+%28DISTANCE%29%2F%28TIME%29

T+=+D%2FR which means TIME+=+%28DISTANCE%29%2F%28RATE%29

Note that RATE means AVERAGESPEED

Make this chart:

                    DISTANCE      RATE       TIME
Going                       
Returning                   
Round trip

Fill in both distances as 200 miles, and the average rate
going is 60 mph and the average rate for returning is 40 mph:

                    DISTANCE      RATE     TIME
Going                 200          60       
Returning             200          40      
Round trip

Now the round trip was 200 + 200 = 400 miles going and coming,
so we fill in 400 for the round trip distance: 

                    DISTANCE      RATE     TIME
Going                 200          60       
Returning             200          40      
Round trip            400

Now we fill in the time for going and the time for returning
using the formula for TIME:

T+=+D%2FR which means TIME+=+%28DISTANCE%29%2F%28RATE%29

to fill in the times.

                    DISTANCE      RATE     TIME
Going                 200          60     200/60 
Returning             200          40     200/40
Round trip            400

Then we simplify those fractions for the times:

                    DISTANCE      RATE     TIME
Going                 200          60     200/60 = 31%2F3 
Returning             200          40     200/40 = 5 
Round trip            400

Now we find the time for the round trip by adding the time going
and the time for returning. 31%2F3 + 5 hours = 81%2F3 hours
for the round trip:

                    DISTANCE      RATE     TIME
Going                 200          60     31%2F3 
Returning             200          40     5 
Round trip            400                 81%2F3 
 
Now we use R=D%2FT to find the average rate, or average speed,
for the round trip:

R+=+D%2FT

      400             400
R = --------     = ---------   = 400 × 3%2F25 = 1200%2F25 = 48 mph
      81%2F3              25%2F3

                    DISTANCE      RATE     TIME
Going                 200          60     31%2F3 
Returning             200          40     5 
Round trip            400          48     81%2F3 

So the answer for the average speed on the round trip is 48 mph.

Edwin