Mr. Jones got his car washed at super clean. The wash started at 1:55pm and ended at 2:05pm. It cost $7. Mr. Smith got his car washed at Super Clean for $12. the wash started at 9:30am and ended at 9:50 am. Write an equation for the line that represents this situation.
Part 2: Use the equation to figure out the cost of Mr. Blie car washed in 30 minute.
Please explain and show work.
To write an equation for the line that represents this situation, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, it represents the cost of the car wash (y) as a function of the time taken for the wash (x) in minutes.
First, let's find the slope (m) of the line. The slope is found by taking the change in y divided by the change in x. For Mr. Jones, the start time is 1:55 pm, which is equivalent to 13:55 on a 24-hour clock. The end time is 2:05 pm, or 14:05 on a 24-hour clock.
The time difference for Mr. Jones is 14:05 - 13:55 = 10 minutes. The corresponding cost difference is $7 - $0 = $7. Therefore, the slope (m) is 7/10 or 0.7.
Next, let's find the y-intercept (b) for the line. For Mr. Smith, the start time is 9:30 am, which is equivalent to 9:30 on a 24-hour clock. The end time is 9:50 am, or 9:50 on a 24-hour clock.
The time difference for Mr. Smith is 9:50 - 9:30 = 20 minutes. The corresponding cost difference is $12 - $0 = $12. Therefore, the y-intercept (b) is $12.
Now, we can write the equation for the line:
y = mx + b
y = 0.7x + 12
To find the cost of a car wash in 30 minutes (x = 30), we can substitute x = 30 into the equation:
y = 0.7(30) + 12
y = 21 + 12
y = 33
Therefore, the cost of Mr. Blie's car wash in 30 minutes would be $33.