SOLUTION: "A truck driver traveled at an average speed of 56 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 s

Question 1153814: "A truck driver traveled at an average speed of 56 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 37 miles per hour. Find the average speed for the
round trip."
That is the question, and the answer is 44.6mi/hr.
But I don't know how to get to that answer.
Found 4 solutions by josgarithmetic, ikleyn, Edwin McCravy, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE PICKUP 56 200/56 200 LOADED 37 200/37 200 TOTAL 400

The average speed for the whole ROUND-TRIP is .
Simplify and compute that.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

There is a general formula = for such problems. Substitute your data into the formula and calculate.

----------------

An amazing fact is that (from this formula point of view), the average speed DOES NOT depend on the total distance (!)

It is THE SAME for any distance and any two-ways returning trip (!)

In this sense, the given distance is IRRELEVANT (!) in this problem (!) (!)

================

See the lessons
    - Calculating an average speed: a train going from A to B and back
    - One more problem on calculating an average speed
in this site.

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
"A truck driver traveled at an average speed of 56 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 37 miles per hour. Find the average speed for the
round trip."

Distance| Rate | Time=Distance/Rate ------------------------------------------------- Going | 200 | 56 | 200/56 hours Returning| 200 | 37 | 200/37 hours ------------------------------------------------- Total | 400 |no need | 200/56 + 200/37 Divide every term in the numerator and denominator by 200 Multiply every term in the numerator and denominator by 56∙37 or 2072 [Something interesting that this problem shows is that the average speed is NOT the average of the speeds, even though the truck traveled at each speed for the same distance, 200 miles. The average of the speeds would be 46.5 mph, which is NOT the right answer!] Edwin

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

Two responses you have received at this point have shown finding the average speed as total distance divided by total time:

That is an ugly kind of calculation that I prefer to avoid.

This is how I would solve the problem.

The ratio of speeds is 56:37; since the distances are the same, the ratio of times is 37:56.

That means the truck driver travels at 56mph for 37/(56+37) of the time and at 37mph for 56/(56+37) of the time. The average speed is then the WEIGHTED average

= 44.56 to 2 decimal places

That to me is an easier calculation for finding the answer.

Note that that calculation is exactly what the other tutor @ikleyn shows in her response: for a round trip at two different speeds, the average speed is

Note that one reason this calculation is easier is that it does not use the given distance. The average speed is independent of the distance -- a point tutor @ikleyn also makes in her response.

So if you were (or are) in a situation where you need to do this kind of calculation frequently, the easiest thing to do is memorize the formula and use it....

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