The math team in addville travled to subtractville for a math compertition. The bus averaged 40 mph from addville to subtractville but adveraged 60 mph during the return trip.
What was the adverage speed of the bus for the entire trip?
Thats the story problem i have to solve. At first i got 50 but then my teacher said it wasn't that and that the answer was harder to find. I think it has something to do with since the mph there and the mph back are adveraged u can't find the total adverage of two adverages(well you can but not in this problem) that somehow you have to find the starting mph that you would adverage.
I need help!
You cant just average the velocities.
Let d be the distance one way
avgspeed=totaldistance/totaltime
but time is time going + time coming back
time going=d/40 and time coming back=d/60
avgspeed=2d/(d/40 + d/60)
multipy the right side by 2400/2400
avgspeed=2*2400d/(60d+40d)
that ought to give it directly.
To find the average speed of the bus for the entire trip, we need to calculate the total distance traveled and the total time taken.
Let's assume the distance between Addville and Subtractville is D miles.
During the trip from Addville to Subtractville, the bus traveled at an average speed of 40 mph. Therefore, the time taken for this leg of the journey can be calculated using the formula: time = distance / speed.
So, the time taken for the trip from Addville to Subtractville is D / 40.
During the return trip from Subtractville to Addville, the bus traveled at an average speed of 60 mph. The time taken for this leg of the journey is D / 60.
Now, to find the total time taken for the entire trip, we need to add the time taken for the outbound journey and the return journey: (D / 40) + (D / 60).
The total distance traveled for the round trip is 2D (since the bus travels the same distance both ways).
To find the average speed of the entire trip, we use the formula: average speed = total distance / total time.
Therefore, the average speed of the bus for the entire trip is:
average speed = (2D) / ((D / 40) + (D / 60))
To simplify this expression, we can find a common denominator for the fractions in the denominator and then merge them:
average speed = (2D) / ((3D + 2D) / (120))
Now, we can simplify the expression:
average speed = (2D) * (120 / (3D + 2D))
average speed = (240D) / (5D)
average speed = 48 mph
So, the average speed of the bus for the entire trip is 48 mph.