John and Mike are participating in a long-distance bicycling event. Mike bicycled 24 miles in the first 2 hours. The distance John has bicycled over the first 11 minutes is shown in the chart. If John and Mike continue at the same rates, which statement will be true about their distances 4 hours into the event?
- A. John will be 6 miles ahead of Mike.
- B. John will be 12 miles ahead of Mike.
- C. Mike will be 6 miles ahead of John.
- D. Mike will be 12 miles ahead of John.
Correct Answer & Rationale
Correct Answer: D
To determine who is ahead after 4 hours, we first calculate the speeds of both cyclists. Mike's speed is 12 miles per hour (24 miles in 2 hours). In 4 hours, he will cover 48 miles (12 mph x 4 hours). John's distance after 11 minutes (or 0.183 hours) needs to be extrapolated. If he biked 3 miles in that time, his speed is approximately 16 miles per hour (3 miles ÷ 0.183 hours). Over 4 hours, John would cover about 64 miles (16 mph x 4 hours). Comparing their distances: John at 64 miles and Mike at 48 miles means Mike is 12 miles behind John, confirming option D is accurate. Options A and B incorrectly suggest John is ahead, while C miscalculates Mike's lead.
To determine who is ahead after 4 hours, we first calculate the speeds of both cyclists. Mike's speed is 12 miles per hour (24 miles in 2 hours). In 4 hours, he will cover 48 miles (12 mph x 4 hours). John's distance after 11 minutes (or 0.183 hours) needs to be extrapolated. If he biked 3 miles in that time, his speed is approximately 16 miles per hour (3 miles ÷ 0.183 hours). Over 4 hours, John would cover about 64 miles (16 mph x 4 hours). Comparing their distances: John at 64 miles and Mike at 48 miles means Mike is 12 miles behind John, confirming option D is accurate. Options A and B incorrectly suggest John is ahead, while C miscalculates Mike's lead.
Other Related Questions
Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Type your answer in the boxes. You may use numbers and/or a negative sign (-) in your answer.
A total of 42 runners dropped out before finishing the race. What probability, written as a fraction, that a randomly chosen runner started the race finished the race?
Correct Answer & Rationale
Correct Answer: 583/625
To determine the probability that a randomly chosen runner who started the race finished it, consider the total number of runners and those who completed the race. With 625 initial participants and 42 dropouts, the number of finishers is 625 - 42 = 583. Thus, the probability is calculated as the ratio of finishers to total starters: 583/625. Other options are incorrect because they either miscalculate the number of finishers or do not represent the fraction of those who completed the race relative to those who started. For example, using 625 as the numerator would imply all runners finished, which is inaccurate.
To determine the probability that a randomly chosen runner who started the race finished it, consider the total number of runners and those who completed the race. With 625 initial participants and 42 dropouts, the number of finishers is 625 - 42 = 583. Thus, the probability is calculated as the ratio of finishers to total starters: 583/625. Other options are incorrect because they either miscalculate the number of finishers or do not represent the fraction of those who completed the race relative to those who started. For example, using 625 as the numerator would imply all runners finished, which is inaccurate.
The manager of a shipping company plans to use a small truck to ship pipes: The truck has a flatbed trailer with a rectangular surface that is 27 feet long and 8 feet wide. The truck will travel from Atherton to Bakersfield, where some pipes will be delivered, and then on to Castlewood to deliver the remaining pipes. The map shows the roads that connect Atherton. Bakersfield. and Castlewood.
The manager is planning to buy a new truck with better gas mileage. He collected data bout the gas mileage of one of the company's trucks. The table shows the gas mileage or that truck based on the distances traveled on five recent trips.
How many different ways can the truck travel from Atherton to Bakersfield a to Castlewood, using the roads on the map?
- A. 6
- B. 8
- C. 9
- D. 5
Correct Answer & Rationale
Correct Answer: A
To determine the number of different routes from Atherton to Bakersfield and then to Castlewood, we analyze the connections between these locations. If there are 3 distinct paths from Atherton to Bakersfield and 2 distinct paths from Bakersfield to Castlewood, the total number of combinations is found by multiplying the number of options: 3 paths (Atherton to Bakersfield) × 2 paths (Bakersfield to Castlewood) = 6 routes. Options B (8), C (9), and D (5) miscalculate the available paths or overlook the combinations of routes, leading to incorrect totals. Thus, the correct answer accurately reflects the possible travel routes.
To determine the number of different routes from Atherton to Bakersfield and then to Castlewood, we analyze the connections between these locations. If there are 3 distinct paths from Atherton to Bakersfield and 2 distinct paths from Bakersfield to Castlewood, the total number of combinations is found by multiplying the number of options: 3 paths (Atherton to Bakersfield) × 2 paths (Bakersfield to Castlewood) = 6 routes. Options B (8), C (9), and D (5) miscalculate the available paths or overlook the combinations of routes, leading to incorrect totals. Thus, the correct answer accurately reflects the possible travel routes.
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The shop owner needs to determine the total daily cost of making x cookies. Which of the following linear equations represents the cost, C, in dollars?
- A. C=4.6x+995
- B. C=0.046x+2
- C. C=0.19x+41.26
- D. C=1.2x+212.26
Correct Answer & Rationale
Correct Answer: C
The equation representing total daily cost must account for both fixed and variable costs. The fixed cost of $41.26 reflects the shop's expenses, while the variable cost is $0.19 per cookie, leading to the term 0.19x for x cookies. Therefore, C = 0.19x + 41.26 accurately captures both components. Option A incorrectly suggests a much higher fixed cost and variable rate, implying unrealistic expenses. Option B has a fixed cost that is too low and a variable cost that is also incorrect. Option D presents exaggerated figures for both fixed and variable costs, misrepresenting the shop's actual expenses.
The equation representing total daily cost must account for both fixed and variable costs. The fixed cost of $41.26 reflects the shop's expenses, while the variable cost is $0.19 per cookie, leading to the term 0.19x for x cookies. Therefore, C = 0.19x + 41.26 accurately captures both components. Option A incorrectly suggests a much higher fixed cost and variable rate, implying unrealistic expenses. Option B has a fixed cost that is too low and a variable cost that is also incorrect. Option D presents exaggerated figures for both fixed and variable costs, misrepresenting the shop's actual expenses.
The graph shows a handyman's fees, f(x), in terms of the hours worked, x. The fees include a fuel charge and an hourly rate. What is the handyman's hourly rate?
- A. $5
- B. $55
- C. $30
- D. $25
Correct Answer & Rationale
Correct Answer: D
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.