Average speed with an unknown distance

[yorick]

[SOLVED] Average speed with an unknown distance

You travel from Place A to Place B, half the time at a speed of 60km/h and the other half at 100km/h. On the return journey, you travel half the distance at 60km/h, and the other half at 100km/h.

a) What is your average speed from A to B?

b) What is your average speed from B to A (return journey)?

c) What is your average speed for the entire trip?



a) $$\overline{Sp}$$ = (60 + 100)/2 = 80km/h... Easy enough.


b&c)
I just don't know where to start with this.
I tried a displacement vs. time graph but without any actual values for the displacement I didn't know what to do.

I'm not necessarily after an answer for this, but a nudge in the right direction would be greatly appreciated.

Thanks,
Yorick.

 

[yorick]

Okay so I've been playing around a bit more, substituting values for displacement.

This is for b)

Letting x=100km,
I travel 50km @ 60km/h = 50min = 5/6 h
and 50km @ 100kmh/h = 30min = 1/2 h

Then $$\bar{Sp}$$ = Distance traveled / (t$$_{2}$$ - t$$_{1}$$) right?

So t2 would be 5/6 + 1/2, t1=0

then $$\bar{Sp}$$ = 100 / (4/3)
=75 km/h




Let x=200km
100km @ 60km/h = 100min = 10/6 h
100 km @ 100km/h = 1 h

then $$\bar{Sp}$$ = 200 / (16/6)
=75km /h

Valid reasoning?
PS sorry for bad Latexing, my subscripts came out as superscript so I gave up.

 

[mysqlpress]

Indeed, it is possible to calculate out .
t= 1/2s/60 +1/2s/100= s/120+s/200
v=s/t = s/(s/120+s/200) = 75km h^-1

c) just easy , A->B = the same distance.
you have the average speeds for both sides...