Math Problem Statement
Jack ran at 880 ft/min for the first 10 minutes of the 3 mile race before slowing his pace to finish the race with a total time of 20 minutes. What was his pace (in feet per minute) for the second part of the race?
Solution
To solve this problem, let's break down the information provided.
Step 1: Calculate the Total Distance of the Race in Feet
Since Jack is running a 3-mile race, we first convert the total distance from miles to feet:
Step 2: Calculate the Distance Covered in the First 10 Minutes
Jack runs at a pace of 880 feet per minute for the first 10 minutes:
Step 3: Calculate the Remaining Distance
Now, we subtract the distance covered in the first part from the total distance to find the distance Jack ran in the second part of the race:
Step 4: Calculate the Time Spent in the Second Part of the Race
Jack's total time for the race is 20 minutes, and he ran the first part in 10 minutes, so the time he spent on the second part is:
Step 5: Calculate the Pace for the Second Part
Now we can find Jack's pace for the second part by dividing the remaining distance by the time for the second part:
Answer
Jack’s pace for the second part of the race was 704 feet per minute.
Would you like further explanation or have any questions about this solution?
Here are 5 related questions for further practice:
- If Jack ran the entire 3-mile race at 880 feet per minute, how long would it take him to finish?
- How much time would Jack save if he maintained his initial pace for the entire race?
- If Jack ran a 4-mile race at the same paces as described, what would his total time be?
- How far would Jack cover if he maintained the slower pace (704 ft/min) for 15 minutes?
- If another runner finished the race in 18 minutes, what was their average pace?
Tip: When working with mixed units, like miles and feet, convert everything to a single unit to simplify calculations.
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Math Problem Analysis
Mathematical Concepts
Distance, Rate, and Time
Unit Conversion
Algebra
Formulas
Distance = Rate × Time
Conversion from miles to feet: 1 mile = 5280 feet
Theorems
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Suitable Grade Level
Grades 6-8