A car travels from A to B. The car averaged 40 mph from A to B but averaged 60 mph during the return trip...?

Question

...What was the average speed of the bus for the entire trip?

Answer 1

suppose the distance from A to B was 120 miles

from A to B, it took 120 / 40 = 3 hours

from B to A, it took 120 /60 = 2 hours

therefore, the total distance was 120 + 120 = 240 miles

total time was 3 + 2 = 5 hours

average speed = total distance / total time

average speed was 240 / 5 = 48 mph

this is a weighted average, weighted by the time at each speed

you spend more time at a slower speed, thus the average is closer to 40 than to 60

Note:  you could pick some constant D to represent the distance, and the average speed would work out the same.  120 was chosen arbitrarily because the times worked out nicely, but you would get the same answer with any distance.

Answer 2

OK. Good Problem.

[Here you cannot just take the average of the 2 speeds, it will be incorrect]

Average speed = Total Distance / Total Time  ...(i)

Distance from A to B = S (suppose)

Total Distance = 2S

Now, Time taken from A to B = S / 40   [ time = distance / speed ]

Time Taken from B to A = S / 60

Now substitute the above values in (i)

Average Speed = 2S / (S / 40 + S / 60)

= 2 / (1 / 40 + 1 / 60)

Average speed = 48 mph

Answer 3

Let distance be d miles from A to B

t 1 = d / 40 hours

t 2 = d / 60 hours

t = t 1 + t 2

t = d / 40 + d / 60 hours

t = (3d + 2d) / 120 hours

t = 5 d / 120 hours

Average speed = 2 d / (5 d / 120 ) mph

Average speed = 240 / 5 mph

Average speed = 48 mph

Answer 4

(40 + 60)/ 2 = 50mph

Answer 5

find the Harmonic mean of 40 and 60

=[2*40*60]/100

=48mph

Answer 6

48 mph

Answer 7

Let the distance between A and B be x, then the time taken forward is x/40 and that for return is x/60.

Average speed

= total distance / total time

= 2x / (x/40 + x/60)

= 2 / (1/40 + 1/60)

= 2 / (5/120)

= 48 mph

Answer 8

see this is a common mistake most people say it 50 mph but thats not how its works

first of all you know the formula distance/time = speed.

so the overall speed for the round trip is the total distance/total time.

lets call the distnace between a and b ,x.

No from a to b the car went  40mph for distance x so the time it took was x/40 and on the way back the time it took was x/60 becuase it went at 60mph for distance x

so the total time is (x/60)+(x/40)=(2x/120)+(3x/120)=(5x/120)...

the total distance is just twice the distance between a and b which is 2x

so to get the total speed you need the total distance 2x

divided by the total time (x/24) but remember that division is multiplication of the reciprocal so you get 2x*(24/x) the x's cancel out and your get 48 mph as teh average

Answer 9

Time going from A to B = AB/40

Time going from B to A = AB/60

Total time from A toB to A = AB/40+AB/60 = 5AB/120

So average = 2AB*120/5AB = 48mph