The equation y = 43x represents the number of miles Alicia drives over time, where y is the number of miles and x is time in hours. This table shows the number of miles Trish drives over time.
How many miles does each woman travel per hour, and who drives at a slower rate?
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Alecia drives at
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mph and Trish drives at
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mph. Alecia drives at a
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rate than Trish.
Trish
Time (h) Miles driven
1.5 69
3.5 161
6 276
7.5 345
Alecia drives at 43 mph and Trish drives at <strong>46 mph</strong>. Alecia drives at a <strong>slower</strong> rate than Trish.
To find the rate at which Alicia and Trish drive, we can calculate the miles each woman travels per hour by dividing the number of miles by the time in hours for each data point in the table.
For Trish:
- For the first data point (1.5 hours, 69 miles), the rate is 69 miles / 1.5 hours = 46 miles per hour.
- For the second data point (3.5 hours, 161 miles), the rate is 161 miles / 3.5 hours = 46 miles per hour.
- For the third data point (6 hours, 276 miles), the rate is 276 miles / 6 hours = 46 miles per hour.
- For the fourth data point (7.5 hours, 345 miles), the rate is 345 miles / 7.5 hours = 46 miles per hour.
From the calculations above, we can see that Trish consistently drives at a rate of 46 miles per hour.
For Alicia:
The equation representing Alicia's number of miles driven over time is y = 43x. Since we do not have any specific time values in the table for Alicia, we cannot directly calculate her rate.
Therefore, we cannot determine Alicia's rate of miles driven per hour based on the given table.
To summarize the information we have:
- Trish drives at a constant rate of 46 miles per hour.
- We do not have sufficient information to determine Alicia's rate of miles driven per hour.
To find the number of miles each woman drives per hour, we need to calculate the rate at which they drive. This can be done by dividing the number of miles by the time in hours.
For Alicia:
- We are given the equation y = 43x, where y represents the number of miles and x represents time in hours. In this case, x is the time in hours.
- We can substitute the given values of x into the equation to find the number of miles at each time point.
- For example, when x = 1.5, we have y = 43 * 1.5 = 64.5 miles.
- Similarly, when x = 3.5, y = 43 * 3.5 = 150.5 miles.
- We can continue this process for all the given time points to find the corresponding number of miles.
For Trish:
- We are given a table that shows the number of miles Trish drives over time.
- By finding the difference in miles between consecutive time points, we can calculate the number of miles Trish drives in each hour.
- For example, between 1.5 hours and 3.5 hours, Trish drives 161 - 69 = 92 miles in 2 hours. This gives us a rate of 92 miles / 2 hours = 46 miles per hour.
- By following the same approach for the other time intervals, we can find the rate at which Trish drives in each hour.
Now, let's calculate the rates for each woman and determine who drives at a slower rate.
- For Alicia:
- When x = 1.5 hours, y = 64.5 miles.
- When x = 3.5 hours, y = 150.5 miles.
- When x = 6 hours, y = 258 miles.
- When x = 7.5 hours, y = 322.5 miles.
- For Trish:
- Between 1.5 and 3.5 hours, Trish drives 92 miles in 2 hours, giving a rate of 46 miles per hour.
- Between 3.5 and 6 hours, Trish drives 276 - 161 = 115 miles in 2.5 hours, giving a rate of 115 miles / 2.5 hours = 46 miles per hour.
- Between 6 and 7.5 hours, Trish drives 345 - 276 = 69 miles in 1.5 hours, giving a rate of 69 miles / 1.5 hours = 46 miles per hour.
From the calculations, we can see that both Alicia and Trish drive at a rate of 46 miles per hour. Neither of them drives at a slower rate.