Av Speed

[Dee-M-See]

On a motor bike course you do 8 laps

Two at 100mph,Two at 102mph, Two at 140mph,and finally Two at 150mph what is your average speed for 8 laps

[Bowler900]

148 mph (unless it's a catch question...)

[Andy Cheever]

119mph, using Time = Distance/Velocity (Distance is a constant)

4 x 1/(1/100 + 1/102 + 1/140 + 1/150)

[hd36kc]

123 mph

[ermintrude35]

...126 mph... ??

( 100+102+140+150 =492, 492/4= 126)..

[ermintrude35]

...sorry meant 123mph*

[Andy Cheever]

Bowler - as a matter of interest how did you arrive at 148
hd36kc, your figure of 123 is simply the average of the four velocities. You can't average this way because the time taken to do each of the four pairs of laps is different in each case. I think you'll find 119 is the correct answer.

[geo0939]

One more for 123 mph.

[Munden]

I'm one for the 119mph

[geo0939]

I think 8 laps is the red herring, surely the answer would be the same for 4 laps?

[don1]

Can someone please explain to this math thickie why the answer isn't simply 123 mph?

[sgeandhu]

suppose the lap is 100 miles round

2 at 100mph = 2hours = 120 mins

2 at 102 mph = 117.6min

2 at 140 mph = 85.7 min

2 at 150 mph = 80 mins

= 800 miles in 403 mins

= 119 mph

[Fibonacci]

Average speed is dependent on time taken and distance travelled.
Take an easier example than the one which was given originally - you have a circuit of 30 miles which you lap at an average speed of 20 mph and then lap again at an average speed of 30mph.
The average speed is NOT (60+30)/2 = 45mph

The total time taken for the two laps
Distance Speed Time taken
Lap 1 30miles 60mph 30/60=0.5h
Lap 2 30 miles 30mph 30/30 = 1h
Total 60miles = 1.5h
Average speed for both laps = total distance / total time taken= 60 / 1.5h = 40mph

Note
If you travel for one hour at constant speed of 60mph and then a second hour at a constant speed of 30mph. Then the usual averaging method ([60+30]/2=45) will work as the time taken for each part of the journey is the same.

The question that started this thread does indeed have an average speed of 119mph.

[Fibonacci]

apologies mistake in my first posting speeds were meant to be 60mph and 30mph (incorrecly typed 20mph instead of 60mph in line 5)

[don1]

Thanks, I've got there even if I was late.

[Bowler900]

Andy Cheever. I got to the answer by the simple expedient of not being able to add up properly :)

On the same basis but using the correct addition, I would say 123 mph, but having seen some of the other, more detailed answers, I am probably wrong with that answer too.

[nijaxx]

Of course Andy Cheever got it right. Enough, please!