hard issue

Question

I'm having a hard time understanding the reason for something.

"If Lucy walks to work at a rate of 4 mph, and she walks home by the same route at a rate of 6 mph, what is Lucy's average walking rate for the round trip ?"

So the problem never establishes a specific distance. Apparently, her average walking rate doesn't depend on the distance (I tried with some different values for the distance and yeah I got the same answer every time). But why? What's the logic behind that? I can't seem to get it.

Please help !

pushpitkc · Answer

Hi  havana97

When she walks a specific distance to her office and the same distance back, it is
safe to say that the distance traveled on both sides is the same. If 2x is the total
distance traveled, x is the distance from home to office and x is the distance from
office to home

Rate(Speed) while traveling from office to home is 4mph, whereas the speed while
traveling from home to office is 6mph. Here, the time taken to travel the distances
are  \frac{x}{4}  and  \frac{x}{6}  respectively.

Total time taken is  \frac{x}{4} + \frac{x}{6} = \frac{10x}{24}  
Distance travelled is 2x

Therefore, the average rate(total distance/total time) is  \frac{2x}{(\frac{10x}{24})}  = 4.8
 
So, as you see the final answer for average rate does not depend on the distance
traveled and that is the reason the answer does not change.

Hope this clears your confusion!

akela · Answer

Hi havana97 , The post above explained the concept perfectly. If you want to read more on average speed, click the following link: https://gmatclub.com/forum/average-spee ... 40271.html Hope this helps!

JaeTPU · Answer

As long as you can set both distances in terms of one unknown (in this case the distances are equal, so we can call both of them x), the time you spent travelling both distance will depend only on speed, not the distance. You can see this in the algebra below:

distance from home to work = x

Average speed = total distance/total time = 2x/(x/4+x/6) =2x/x(1⁄4+1⁄6) = 2/(1⁄4+1⁄6) = 4.8 as you can see x cancels out.

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