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22 Jun 2023, 01:30
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D
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Difficulty:
35%
(medium)
Question Stats:
68% (02:40) correct
32%
(02:36)
wrong
based on 77
sessions
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Madonna is driving from a hotel to a concert hall. After passing a quarter of the way she accelerates, so that her average speed for the rest of the way is 50% faster than the average speed for the first quarter. If Madonna's average speed for her entire way from the hotel to the concert is 80 kilometers per hour, what is her average speed in kilometers per hour for the first quarter of her way?
A. 33 1/3
B. 40
C. 50
D. 60
E. 66 2/3
A. 33 1/3
B. 40
C. 50
D. 60
E. 66 2/3
22 Jun 2023, 04:20
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Asked: Speed during the first quarter.
Given: Speed in quarter 1 = "s", Speed in quarter 2 = "1.5s", Total Average Speed = 80 Kmph.
Solution: Assume the total Distance to be "D"
------ "D/4" Distance covered in speed "s" ------ "3D/4" Distance covered in speed "1.5s" ------
We can use the formula of Average Speed = \(\frac{Total Distance}{ Total Time.}\)
80 = D/(D/4s + 3D/4*1.5s) ( The Distance gets cancelled )
On solving, we get -> 4s/3 = 80 -> s = 60 Kmph.
Answer: D
Given: Speed in quarter 1 = "s", Speed in quarter 2 = "1.5s", Total Average Speed = 80 Kmph.
Solution: Assume the total Distance to be "D"
------ "D/4" Distance covered in speed "s" ------ "3D/4" Distance covered in speed "1.5s" ------
We can use the formula of Average Speed = \(\frac{Total Distance}{ Total Time.}\)
80 = D/(D/4s + 3D/4*1.5s) ( The Distance gets cancelled )
On solving, we get -> 4s/3 = 80 -> s = 60 Kmph.
Answer: D
22 Jun 2023, 05:30
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Let's call the total distance from the hotel to the concert hall "d". Madonna passes a quarter of the way, which means she has traveled d/4 distance. This leaves 3d/4 distance for the rest of the way.
Let's call Madonna's average speed for the first quarter "x". Then her average speed for the rest of the way is 1.5x (50% faster than x).
We can use the formula:
average speed = total distance / total time
To solve for x, we need to find the total time it takes Madonna to travel from the hotel to the concert hall.
For the first quarter, the time it takes is:
time = distance / speed = (d/4) / x = d/4x
For the rest of the way, the time it takes is:
time = distance / speed = (3d/4) / 1.5x = d/2x
The total time it takes is the sum of these two times:
total time = d/4x + d/2x = 3d/4x
Now we can use the formula for average speed:
80 = d / (3d/4x)
80 = 4x/3
x = 60
Answer is option D.
Let's call Madonna's average speed for the first quarter "x". Then her average speed for the rest of the way is 1.5x (50% faster than x).
We can use the formula:
average speed = total distance / total time
To solve for x, we need to find the total time it takes Madonna to travel from the hotel to the concert hall.
For the first quarter, the time it takes is:
time = distance / speed = (d/4) / x = d/4x
For the rest of the way, the time it takes is:
time = distance / speed = (3d/4) / 1.5x = d/2x
The total time it takes is the sum of these two times:
total time = d/4x + d/2x = 3d/4x
Now we can use the formula for average speed:
80 = d / (3d/4x)
80 = 4x/3
x = 60
Answer is option D.
