Question

Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be filled, and after 5 minutes, he had 25 cups left to be filled. Mary’s progress is shown in the table of values below. Assuming that both Jorge and Mary are filling cups at a constant rate, which statement is correct?


Mary’s Cup-Filling Progress
Time (minutes)
0.5
1
1.5
2
2.5
Cups Remaining
99
81
63
45
27
Jorge is filling 14 cups per minute, which is faster than Mary.
Jorge is filling 28 cups per minute, which is faster than Mary.
Mary is filling 18 cups per minute, which is faster than Jorge.
Mary is filling 36 cups per minute, which is faster than Jorge.

Answer 1

Required Answer:

The above data gives us information about the relative time taken by two kids Jorge and Mary for filling the cups.

GiveN:

• After 3 min, Jorge is left with 53 cups.
• After 5 min, Jorge is left with 25 cups.

So, we can see that, between the time interval of 3 and 5 minutes, Jorge is filling 53 - 25 = 28 cups. This means:

$\sf{ \longrightarrow{2 \: minute = 28 \: cups}}$

Then,

$\sf{ \longrightarrow{1 \: minute = 14 \: cups}}$

So the speed of Jorge in filling the cups is 14 cups per minute. Now, let's see for Mary.

GiveN:

• 0.5 minutes = 99 remaining
• 1 minutes = 81 remaining
• 1.5 minutes = 63 remaining
• 2 minutes = 45 remaining
• 2.5 = 27 remaining

So, we can see here, between there is a time interval of 0.5 minutes, and Mary is filling 99 - 81 = 18 cups. This rate is uniform.

$\sf{ \longrightarrow{1 \: minute = 18 \times 2 = 36 \: cups}}$

Hence, Mary is filling the cups at a greater speed as compared to Jorge. And this is by:

"Mary is filling 36 cups per minute, which is faster than Jorge."

$\large{\therefore{\underline{\boxed{\gray{\bf{Option D}}}}}}$

And we are done !!

Answer 2

$\bold{Questions: }$

The above data gives us information about the relative time taken by two kids Jorge and Mary for filling the cups.

GiveN:

After 3 min, Jorge is left with 53 cups.

After 5 min, Jorge is left with 25 cups.

So, we can see that, between the time interval of 3 and 5 minutes, Jorge is filling 53 - 25 = 28 cups. This means:

⟶2minute=28cups

Then,

⟶1minute=14cups

So the speed of Jorge in filling the cups is 14 cups per minute. Now, let's see for Mary.

GiveN:

0.5 minutes = 99 remaining

1 minutes = 81 remaining

1.5 minutes = 63 remaining

2 minutes = 45 remaining

2.5 = 27 remaining

So, we can see here, between there is a time interval of 0.5 minutes, and Mary is filling 99 - 81 = 18 cups. This rate is uniform.

⟶1minute=18×2=36cups

Hence, Mary is filling the cups at a greater speed as compared to Jorge. And this is by:

"Mary is filling 36 cups per minute, which is faster than Jorge."

$\bold{ANSWER : }$ OptionD

And we are done !!