Race Average

[Dee-M-See]

In a cycle race a rider averaged 20mph on the outward leg and 30mph on the return leg what was his overall average speed?

[amalgam]

I think it's 24 mph, tho maths is not my strong point

[grasscarp]

I would have though 25 if he did 30 and 20 for the same distance.

[Hammond Egg]

Amalgam is right, the answer is 24mph

Its called the harmonic mean.

Assume each leg of the ride was 3 miles

On the outward leg he rides at 20mph, so each mile will take him 3 minutes; the total time for the outward leg would be 3x3 = 9 minutes

Coming back he rides the 3 miles at 30 mph, so each mile of the journey takes him 2 minutes; the total time for the return leg is 3 x 2 = 6 minutes

SO the total time for the total journey of 6 miles would be 15
minutes

Which make his average speed 24mph

[amalgam]

if, say, the course was 30 miles long, he would take 1 1/2 hours over the outward leg, and 1 hour over the return leg. That is, 2 1/2 hours to do 60 miles in total. 60 divided by 24 equals 2 1/2, doesn't it? Now I really am getting muddled, aren't I? Or am I?

[THECORBYLOON]

If there are two speeds, A and B, the average speed over the two legs is 2(A x B)/(A + B)

[Hammond Egg]

It does, but you should have the last equation the other way round - it should be 60(miles) divided by 2� (hours) to give the answer 24 mph

[Hammond Egg]

My last post was in reply to amalgam

TCL is right, as he usually is!