A car covers some distance at a speed of 100 km/h, and then it returns back the same distance at a speed of 60 km/h. what would be the average speed for this car.
hint: the correct answer is 75 but I just don't get it.
2007-03-11 12:25:04 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
If the same distance is covered at two average speeds, b and c, then the reciprocal of the average over the round trip is half the sum of the reciprocals of the individual averages:
1/total_ave = (1/b + 1/c)/2
1/total_ave = (1/100 + 1/60)/2 = 160/(100*60*2) = 1/75
So total_ave = 75.
You could work out this formula by figuring out the time for the total trip given the individual averages, then divide twice the distance by that time.
2007-03-11 13:44:44 · answer #1 · answered by Quadrillerator 5 · 0⤊ 0⤋
The confusion arises when you try taking the average of the speeds. But remember, average speed is not average of the speeds, but total dist/total time.
The times that the two legs of the journeys last is different. Since speed has the time variable in the denominator, the average of two speed values will lead to the right average speed value if the times of travel are different. That is to say when the guy travelled a distance d at 100 kmph he took less time than when he travelled the same distance at 60kmph.
If the problem was - the guy travels for a time t @ 100kmph and for another time t at 60 kmph, then the average speed would be 80kmph.
For further comtemplation, imagine this - suppose on the reverse journey, he travelled at the speed of light and reached back in negligible time. would the average speed be close to half the speed of light????? nay....at max it would be double the onward journey speed. right??
2007-03-12 03:13:26 · answer #2 · answered by FedUp 3 · 0⤊ 0⤋
Speed = Distance/Time
Time = Dist. / Speed
Time for forward direction = 100/100 = 1 hr.
Time for backward direction = 100/60 = 1. 6666 hr.
Avg. Speed = Total Distance/Total time
= (Dist. going forward + Dist. coming back)/(Time going forward + Time coming back)
= (100 + 100) / (1 + 1.6666)
= 200 / 2.6666
=75 km/hr.
2007-03-14 12:44:10 · answer #3 · answered by Pranil 7 · 0⤊ 0⤋
let us assume the distance is 100 (one way) then total distance is 200 km
time taken @ speed of 100km/hr is 1 hr
time taken @ speed of 60k/hr is 1.6666667 ( 100/60)
to average speed is 200/ 2.666667 = 75.
please note it can vary slightly in points ....depens how you take 2.66667 or 2.67 or 2.6666666666667
2007-03-11 20:45:43 · answer #4 · answered by Ajju 1 · 0⤊ 0⤋
Even i don't get it.Answer could be wrong.
2007-03-14 04:35:17 · answer #5 · answered by Aksum 2 · 0⤊ 0⤋
that's a question you could research yourself. have fun.
2007-03-11 19:41:20 · answer #6 · answered by Anonymous · 0⤊ 0⤋