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Average Speed

Math brain teasers require computations to solve.

 

Puzzle ID:#960
Fun:*** (2.35)
Difficulty:** (1.83)
Category:Math
Submitted By:Michelle***

 

 

 



A car travels at a speed of 30 mph over a certain distance, and then returns over the same distance at a speed of 20 mph. What is the average speed for the total trip?

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Comments

Sane**
Mar 12, 2005

It's weird, there is something about these kind of teasers I find hard. Yet the really difficult rated teasers I do fine on.
Maslin
Jun 09, 2005

I dont understand what time has to do with it. Also would you reach the same answer if the traveled distance was 30 miles? I really hope you can explain these to me so I can get really smart
Maslin
Jun 09, 2005

it does work with 30! Now why is time important?
thompson1Aus*
May 23, 2006

You are trying to find the average speed in mpH (which is time). It would work for any amount. If you say it is a 60 mi length, then it would be 120 mi total (there and back) and it would take 5 hours (2h for 30mph + 3h for 20mph), and mph=m/h so 120mi/5h simplifies to 24mi/1h. Get it now? Great teaser, also!
Crazycriely*
Jun 23, 2006

i dont get it
HellColdAeg*
Feb 07, 2009

The answer is correct. But the rule for getting it--directly, without using a virtual distance and calculating from it the average velocity based on total distance per total time--is not stated.


The rule is: [2 (V1.V2) / (V1+V2)] without regard to distance.


Here's how I derived it.
V average = D total/T total

D total is twice D always. (you go and return, covering twice the same distance)

So, V average = 2.D/T total

T total is the sum of T1 (time going) and T2 (time coming back)

So, V average = 2.D/(T1+T2)

Since V = D/T, so T = D/V

V average = 2.D divided by [(D/V1)+(D/V2)]

Take the common factor D

V average = 2 divided by [(1/V1)+(1/V2)]

V average = 2 divided by [(V1+V2)/(V1.V2)]

So, V average = 2(V1.V2)/(V1+V2)

That's it! Good question...
Jimbo*au*
Mar 31, 2009

Hell that's a complicated way to do a simple problem. A much more interesting question is if he travels there at 30 mph , what speed must he do on the return trip to average 60 mph for the round trip?



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