Average speed (harmonic mean) - Need pro to modify formula

Question

I know that if given two 2 values of average speed for 2  identical  distance, I can use 2ab/(a+b)

But what happens if

a) Distance X is twice the second segment Distance Y? I am sure there is a way to modify this formula, replacing the "2" in the original formula to something like "1+(a+b/2a)" ?

b) What happens if there is more than two segments of distance? e.g. 3 average speeds on  identical  distance?

c) Possible to have a very versatile formula to address more than 2 segments AND with varying distances?

mikemcgarry · Answer

Dear Ghostie , I'm happy to respond. :-)

Here's what I'll say. The way to guarantee a mediocre performance on the GMAT Quant section is to try to memorize a formula for every problem. Memorization of formulas can be helpful on the easier problems, but GMAT specializes in writing problems designed to frustrate the memorizers. If memorization of formulas is your primary strategy, you aiming for a not-very-desirable score on the GMAT Quant. Here's what I recommend instead. Take every opportunity to think through everything from first principles. Consider this problem (probably more complicated than the GMAT would give): Herb drives 400 mi at 50 mph, then drives at 60 mph for 5 hours, then drives 500 miles in 7 hours. What is Herb's average speed for the trip? This is actually a relatively easy problem, but it would be pure insanity to try to memorize a formula for something like this. The only formula you need is: average velocity = (total distance)/(total time) The strategy is always (a) find the distance & time of each leg (b) find the total distance by adding (c) find the total time by adding (d) divide To find the total distance & total time, we need the distance and time of each leg of the trip. First leg: D1 = 400, and R = 50, so T1 = 400/50 = 8 hour Second leg: T2 = 5, and R = 60, so D2 = 5*60 = 300 miles Third leg: D3= 500 and T3 = 7 Total distance = D1 + D2 + D3 = 400 + 300 + 500 = 1200 miles Total time = T1 + T2 + T3 = 8 + 5 + 7 = 20 hours Average velocity = 1200/20 = 60 mph You see, that basic strategy will help you in a wide variety of distance-rate-time problems, regardless of how many legs. Thinking through all the details like this will give you a much deeper and more thorough understanding than memorizing special case formulas. Here's a blog about this problem type: https://magoosh.com/gmat/2012/gmat-dista ... e-formula/ Here's a blog about the dangers of memorizing: https://magoosh.com/gmat/2012/gmat-math- ... emorizing/ Here's a blog about the kind of mathematical thinking the GMAT demands: https://magoosh.com/gmat/2013/mathematic ... -the-gmat/ Does all this make sense? Mike :-)

dabral · Answer

I will second what Mike said above, do not memorize these average speed formulas but instead understand how they are obtained. It is very likely that the GMAT will modify the problem statement in a fashion such that the formula is no longer applicable. This is also applicable for machine-work problems which also has a formula for time it takes two machines together to do a given job, which can also be extended to three machines. But again no need to memorize them, but instead be ready to apply the basic relationships in diverse situations.

Dabral

Dabral

ghostie · Answer

As time is limited, I believe memorizing some formulas helps. Of course I can go the long way, but applying formulas really doesnt mean I am doing it blindly.

Average speed (harmonic mean) - Need pro to modify formula

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