Lanelle traveled 9.7 miles of her delivery route in 1.2 hours. At this same rate, which of the following is closest to the time it will take for Janelle to travel 20 miles?
- A. 2 hours
- B. 2.5 hours
- C. 5 hours
- D. 5.5 hours
Correct Answer & Rationale
Correct Answer: B
To determine the time it will take for Janelle to travel 20 miles, we first calculate Lanelle's speed. She traveled 9.7 miles in 1.2 hours, giving a speed of approximately 8.08 miles per hour (9.7 miles ÷ 1.2 hours). Using this speed, we can find the time for 20 miles by dividing the distance by the speed: 20 miles ÷ 8.08 mph ≈ 2.48 hours, which rounds to about 2.5 hours. Option A (2 hours) underestimates the time based on Lanelle's speed. Options C (5 hours) and D (5.5 hours) greatly overestimate the time needed. Thus, 2.5 hours is the most accurate estimate for Janelle's travel time.
To determine the time it will take for Janelle to travel 20 miles, we first calculate Lanelle's speed. She traveled 9.7 miles in 1.2 hours, giving a speed of approximately 8.08 miles per hour (9.7 miles ÷ 1.2 hours). Using this speed, we can find the time for 20 miles by dividing the distance by the speed: 20 miles ÷ 8.08 mph ≈ 2.48 hours, which rounds to about 2.5 hours. Option A (2 hours) underestimates the time based on Lanelle's speed. Options C (5 hours) and D (5.5 hours) greatly overestimate the time needed. Thus, 2.5 hours is the most accurate estimate for Janelle's travel time.
Other Related Questions
For all positive integers n, let n be defined as the sum of the positive divisors of n. For example, bullet 9 = 1 + 3 + 9 = 13. Which of the following is equal to 16 - 15?
- A. 41
- B. 3
- C. 4
- D. 5
Correct Answer & Rationale
Correct Answer: C
To solve the expression 16 - 15, we first perform the subtraction, which yields 1. Now, examining the options: A: 41 is incorrect as it does not equal 1. B: 3 is also incorrect, as it is greater than 1. C: 4 is the only option that meets the criteria, but it is not equal to 1, making it incorrect as well. D: 5 is incorrect for the same reason; it does not equal 1. None of the options accurately represent the result of 16 - 15, which is 1. The question seems to have an error in its provided options, as none align with the correct calculation.
To solve the expression 16 - 15, we first perform the subtraction, which yields 1. Now, examining the options: A: 41 is incorrect as it does not equal 1. B: 3 is also incorrect, as it is greater than 1. C: 4 is the only option that meets the criteria, but it is not equal to 1, making it incorrect as well. D: 5 is incorrect for the same reason; it does not equal 1. None of the options accurately represent the result of 16 - 15, which is 1. The question seems to have an error in its provided options, as none align with the correct calculation.
Fred, Norman, and Dave own a total of 128 comic books. If Dave owns 44 of them, what is the average (arithmetic mean) number of comic books owned by Fred and Norman?
- A. 42
- B. 44
- C. 46
- D. 48
Correct Answer & Rationale
Correct Answer: A
To find the average number of comic books owned by Fred and Norman, first determine how many comic books they collectively own. Since Dave has 44 comic books, subtract this from the total: 128 - 44 = 84. Fred and Norman together own 84 comic books. To find the average for the two, divide this number by 2: 84 ÷ 2 = 42. Option B (44) incorrectly assumes Fred and Norman have more than they actually do. Option C (46) miscalculates the average by not considering the correct total for Fred and Norman. Option D (48) similarly overestimates their combined ownership. Thus, the average is accurately calculated as 42.
To find the average number of comic books owned by Fred and Norman, first determine how many comic books they collectively own. Since Dave has 44 comic books, subtract this from the total: 128 - 44 = 84. Fred and Norman together own 84 comic books. To find the average for the two, divide this number by 2: 84 ÷ 2 = 42. Option B (44) incorrectly assumes Fred and Norman have more than they actually do. Option C (46) miscalculates the average by not considering the correct total for Fred and Norman. Option D (48) similarly overestimates their combined ownership. Thus, the average is accurately calculated as 42.
If |x|+|y| = 4 and x ≠y, then x CANNOT be equal to
- A. 2
- C. -2
- D. -5
Correct Answer & Rationale
Correct Answer: D
The equation |x| + |y| = 4 defines a diamond-shaped region in the coordinate plane, where the sum of the absolute values of x and y equals 4. Option A (2) is possible since |2| + |y| = 4 allows y to be 2 or -2. Option C (-2) is also valid, as |-2| + |y| = 4 permits y to be 2 or -2. Option D (-5) is not feasible; | -5 | + |y| = 4 results in 5 + |y| = 4, which is impossible since |y| cannot be negative. Thus, -5 cannot satisfy the given equation while ensuring x ≠ y.
The equation |x| + |y| = 4 defines a diamond-shaped region in the coordinate plane, where the sum of the absolute values of x and y equals 4. Option A (2) is possible since |2| + |y| = 4 allows y to be 2 or -2. Option C (-2) is also valid, as |-2| + |y| = 4 permits y to be 2 or -2. Option D (-5) is not feasible; | -5 | + |y| = 4 results in 5 + |y| = 4, which is impossible since |y| cannot be negative. Thus, -5 cannot satisfy the given equation while ensuring x ≠ y.
Valentina attends several meetings each day, as shown in the table below. Which of the following describes this pattern?
- A. The number of meetings increases by the same amount each day.
- B. The number of meetings decreases by the same amount each day.
- C. Each day, the number of meetings increases by the same percent over the previous day's number of meetings.
- D. Each day, the number of meetings decreases by the same percent over the previous day's number of meetings.
Correct Answer & Rationale
Correct Answer: C
The pattern of Valentina's meetings indicates that the number of meetings increases by a consistent percentage each day, reflecting exponential growth. This is evident when comparing the daily totals, which show a proportional rise rather than a fixed increase. Option A is incorrect because it suggests a linear growth, where the same number of meetings is added daily, which is not observed. Option B implies a consistent decrease, which contradicts the observed increase in meetings. Option D also misrepresents the data by suggesting a percentage decrease, which does not align with the trend of increasing meetings.
The pattern of Valentina's meetings indicates that the number of meetings increases by a consistent percentage each day, reflecting exponential growth. This is evident when comparing the daily totals, which show a proportional rise rather than a fixed increase. Option A is incorrect because it suggests a linear growth, where the same number of meetings is added daily, which is not observed. Option B implies a consistent decrease, which contradicts the observed increase in meetings. Option D also misrepresents the data by suggesting a percentage decrease, which does not align with the trend of increasing meetings.