Question

Michael and Derek enjoy playing tennis, and before every match they estimate how long it will take. The actual match time is always greater than the time Michael and Derek estimate. They recorded the times for four matches, but some of the information has been lost. Complete the table. Round to the nearest 10th if necessary.

Match Actual Time . Estimate Time . Percent Error
1 2 hours , 90 minutes, unknown.
2 unknown, 1 hour, 25%
3 3 hours , unknown , 15%
4 150 minutes , 75 min. , unknown

Answer 1

Based on the given information, the missing values for Matches 1, 2, 3 and 3 are approximately 25%, 80 minutes, 156.52 minutes and 50%, respectively.

How to determine the missing values

For Match 1:

Actual Time: 2 hours (120 minutes)

Estimated Time: 90 minutes

Percent Error Formula: Percent Error = |(Estimated Time - Actual Time) / Actual Time| * 100

Percent Error for Match 1:

Percent Error = |(90 - 120) / 120| * 100 = |(-30) / 120| * 100 = 30 / 120 * 100 = 25%

For Match 2:

Estimated Time: 1 hour (60 minutes)

Percent Error: 25%

Given the Percent Error is 25%, using the formula to solve for the actual time:

Percent Error = |(Estimated Time - Actual Time) / Actual Time| * 100 = 25%

|(60 - x) / x| * 100 = 25

Solving this equation yields x = 60 / 0.75 ≈ 80 minutes or 1 hour and 20 minutes.

For Match 3:

Actual Time: 3 hours (180 minutes)

Percent Error: 15%

Using the same percent error formula:

Percent Error = |(Estimated Time - Actual Time) / Actual Time| * 100 = 15%

|(x - 180) / 180| * 100 = 15

Solving this equation yields x = 180 / 1.15 ≈ 156.52 minutes or 2 hours and 36.52 minutes.

For Match 4:

Actual Time: 150 minutes

Estimated Time: 75 minutes

Percent Error for Match 4:

Percent Error = |(75 - 150) / 150| * 100 = 50%

Therefore, based on the given information, the missing values for Matches 2 and 3 are approximately 1 hour and 20 minutes and 2 hours and 36.52 minutes, respectively.