SOLUTION: 10) A messenger walks 500 feet in a large building from the reception to his destination at the average speed of 4 miles per hours and returns to the starting point at an average s

Question 543997: 10) A messenger walks 500 feet in a large building from the reception to his destination at the average speed of 4 miles per hours and returns to the starting point at an average speed of 3 miles per hour. What is his average speed for the entire trip ?
It's been 20 plus years since my last math class. More than the answer, I really would like some pointers on how to set up the equations to solve this.
I'm taking an administrative test and math problmes are part of it.
Thanks,
Scott
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1_ Pretend it's not math, and it may become a problem you could easily solve in real life. You probably figure out how long a trip will be when driving somewhere. How do you do it? Distance divided by speed?
2_ Think of a strategy. Divide and conquer. You could calculate how long it took each way in separate calculations first. Then, you could take the total distance, and divide by the total time to get the average speed. That's how you calculate average speed for a trip: total distance divided by total time.
3_ Get smarter and do not kill yourself with unnecessary calculations. Think a bit before you jump into them. This guy's average speed would be the same if the round trip was longer or shorter. Every time and distance number in the calculations would be scaled up the same factor, but the speeds would be the same. What if it was 12 miles each way? It take 3 hours going and 4 coming back, for a total of 7 hours. The 24 miles divided by 7 hours would give you the average speed.
4_ Is it multiple choice? If it is, you got the answer 24/7 or 3 3/7 or about 3.43 miles per hour.
5_ Do you have to show your work? In this case, you can make up a variable or use 1 for all rate of work problems. If you use d for distance the times for the two legs of the trip and the round trip are calculated and related like this
where x is the speed
With common denominator, -->
Divide both sides by 2 and by d
--->

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