Calculating Average Speed from Lap 1 & 2

[NettioB]

Homework Statement

Hi

I read a question recently on the British Mensa website and I thought the answer was 112.5mph. The answer given was 108mph. What is the calculation for this scenario?

"Lap 1 is completed at 135mph, lap 2 is completed at 90mph, what’s the average speed?"

Homework Equations

summation and division of two numbers

The Attempt at a Solution

135 plus 90 equals 225. 225 divided by 2 eqals 112.5


Thanks.

N.

 

[kuruman]

Homework Equations

summation and division of two numbers

Not in this case. Averaging is sometimes tricky. Average speed is defined as total distance traveled divided by total time required to travel that distance. Use this idea and you might be surprised with the result.

 

[NettioB]

The question is located at:

http://twitter.com/BritishMensa/status/20563510467

 

[kuruman]

The question is located at:

http://twitter.com/BritishMensa/status/20563510467

So? Can you do the calculation as I indicated? It requires a little bit of algebra or the realization that is question is entirely analogous to finding the equivalent resistance of two resistors in parallel or the equivalent capacitance of two capacitors in series.

 

[NettioB]

With this information I cannot. We only have two average speeds, one per lap (or two constant speeds, one per lap). We have neither a distance or a time.

 

[kuruman]

We have neither a distance or a time.

Neither of these are needed. Just the knowledge that the laps are of equal length. Start writing something down and see what develops.

Step 1. Can you write an equation for the definition of the average speed that I gave you? Use symbols for quantities that you don't know and have faith that it will all come out in the wash.

 

[NettioB]

If L = lap distance and T1 and T2 = time to travel each lap, we can write:

Average speed = 4L / (T1 + T2)

But I can't get further than this.

 

[kuruman]

It should be

v_ave = 2L/(t₁+t₂) where L is the distance of one lap. The total trip is two laps or 2L.

Step 2: Can you find expressions for t₁ and t₂ in terms of L and v₁ and v₂?

 

[NettioB]

t₁ = v₁ / L

t₂ = v₂ / L

V_avg = 2L² / (v₁ + v₂)

= 2L² / (135 + 90)

= L² / 112.5


Where can I go from here?

 

[kuruman]

t₁ = v₁ / L

t₂ = v₂ / L

No. t₁ = L / v₁ and t₂ = L / v₂.

Step 3: Now add the two times together to get the sum. Be sure to add the fractions correctly on the right side. Replace the sum t₁+t₂ in the equation for v_ave and see what you get.