Math Question

[boy1_]

This is for anyone with any math skills. My calc. class had no homework so the teacher cooked this up for us, even though it isn't calculus.

A car leaves on a trip, it travels at 50km/h on the way there, how fast must the car go on the return trip to have a total average of 100km/h?

As far as I can calculate it is impossible, the return trip would have to occur instantaneously. But I have a feeling i that I am wrong. Any help would be appreciated.

[DefektiveVibe]

its like a riddle...depends on how far the car travelled?

but what i think is that it would be 150km/h because...

50km/h going, 150km/h coming = 200km/h total / 2 ways = 100km/h average

[boy1_]

(what i got)

Velocity average = total distance / total time

say the total distance = 100km, so for the first half (50k) travelling at 50km/h it takes him 1 hour, so 100km/(1 hr+ x hrs) = 100km/h. for this to be true x must be equal to zero, meaning the speed for the second half of the trip must infinite, the second half of trip must occur instantly.)

[V6-BoI]

yeah this is like a trick question.
is the 50km/h a velocity or a speed?

[boy1_]

the real question is "you drive to whistler at 50km/h, you drive home fast enough that your average speed for the whole trip is 100km/h. what was your speed for the return trip?"

i have come to the conclusion that as your average approaches 100km/h your speed for the return trip approaches infinity.

[cman]

assuming the take the exact root and remain at exactly 50k and 150k the whole way, i think the average would be 100k

[1-Bar]

it cannot be 150km/hr because if you judge it by distance, on the return trip you will not be on the road as long since your going faster and covering more distance in a shorter amount of time.....

Lets say its 150km distance @ 50km/hr then @150km/hr (return), so the first trip it will take you 3 hours and the return 1 hour. Total time, 4 hours, today distance traveled, 300km -----> 75km/hr average

Trick question....

[FiveFreshFish]

Originally posted by boy1_
i have come to the conclusion that as your average approaches 100km/h your speed for the return trip approaches infinity.

That's correct.

Think of it this way. Assume the trip is 50 km, so going there takes one hour. The return trip is also 50 km, so the total distance is 2 x 50 = 100 km.

To average 100 km/h for the entire trip, you need to travel that 100 km distance in 1 hour. But you already used up 1 hour on the outgoing trip at 50 km/h, so it's impossible to achieve an average speed of 100 km/h unless your return trip is instantaneous (i.e. infinite speed).

[boy1_]

^^ thats exactly what i did, just wanted a second opinion on the problem