Mario rides his scooter to work each day. He is able to travel 0.5 miles per
He lives 4.7 miles from work.
minute.
a. Copy the table and fill in Mario's distance to work based on the number
of minutes traveled. Continue the table until he has arrived at work.
b. What is the rate of change in this situation?
c. How long (to the nearest second) will it take for Mario to get to work?
Explain how you arrived at your answer.
Minutes
Traveled
0
1
Distance to
Work
4.7
a.
Minutes | Distance to Work
0 | 4.7 miles
1 | 4.2 miles
2 | 3.7 miles
3 | 3.2 miles
4 | 2.7 miles
5 | 2.2 miles
6 | 1.7 miles
7 | 1.2 miles
8 | 0.7 miles
9 | 0.2 miles
10 | Arrived at work
b. The rate of change in this situation is 0.5 miles per minute.
c. To find out how long it will take for Mario to get to work, we need to find the number of minutes it takes for him to travel the distance of 4.7 miles.
Using the rate of change of 0.5 miles per minute, we can set up the proportion:
0.5 miles / 1 minute = 4.7 miles / x minutes
Cross multiplying and solving for x, we get:
0.5x = 4.7
x = 4.7 / 0.5
x = 9.4 minutes
Therefore, it will take Mario approximately 9.4 minutes to get to work.
a. To fill in Mario's distance to work based on the number of minutes traveled, we can use the formula:
Distance = Speed × Time
Given that Mario can travel 0.5 miles per minute, we can fill in the table using this formula:
Minutes Traveled | Distance to Work
0 | 4.7
1 | 4.7 - 0.5 = 4.2
b. The rate of change in this situation represents how the distance to work changes with respect to time. Since Mario's speed is constant at 0.5 miles per minute, the rate of change is also 0.5 miles per minute.
c. To find out how long it will take for Mario to get to work, we can divide the distance to work (4.7 miles) by his speed (0.5 miles per minute):
Time = Distance / Speed
Time = 4.7 / 0.5
Time ≈ 9.4 minutes
To convert minutes to seconds, we need to multiply by 60:
Time (in seconds) ≈ 9.4 × 60
Time (in seconds) ≈ 564
Therefore, it will take approximately 9 minutes and 24 seconds for Mario to get to work.
a. To fill in Mario's distance to work based on the number of minutes traveled, we need to determine how many minutes it will take for him to reach work. We can start by filling in the given information from the problem:
Minutes Distance to
Traveled Work
0 4.7
Now, we know that Mario is able to travel 0.5 miles per minute. So, for every minute he travels, he will be 0.5 miles closer to work.
To find the distance to work for each minute traveled, we can subtract 0.5 miles from the previous distance:
Minutes Distance to
Traveled Work
0 4.7
1 4.2
We can continue this process until Mario reaches work.
Minutes Distance to
Traveled Work
0 4.7
1 4.2
2 3.7
3 3.2
4 2.7
5 2.2
6 1.7
7 1.2
8 0.7
9 0.2
10 -0.3
b. The rate of change in this situation is -0.5 miles per minute, as Mario is moving 0.5 miles closer to work for each minute traveled.
c. To determine how long it will take for Mario to get to work, we need to find the time when the distance to work is 0. We can see from the table that this happens at 10 minutes (when the distance to work is -0.3 miles).
However, a negative distance doesn't make sense in this context, so we can ignore it and focus on the previous value. At 9 minutes, the distance to work is 0.2 miles. Since we know that Mario travels 0.5 miles per minute, we can calculate the remaining time needed to cover the remaining distance:
Time = (Distance to Work) / (Rate of travel)
Time = 0.2 miles / 0.5 miles per minute
Time ≈ 0.4 minutes
To convert this to seconds, we multiply by 60:
Time ≈ 0.4 minutes * 60 seconds/minute = 24 seconds
Therefore, it will take approximately 24 seconds for Mario to get to work.