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Nile River Travel: Calculate Daily Miles and Check Reasonableness
Mathematics
Grade 6
Question Content
Check for Reasonableness: The Nile River is the longest river in the world. It is 4,160 miles long. You want to spend three weeks traveling the entire length of the river, traveling the same number of miles each day. How many whole miles should you travel each day? Use an estimate to check for reasonableness.
Correct Answer
198 whole miles per day
Detailed Solution Steps
1
Step 1: Calculate total travel days: 3 weeks × 7 days/week = 21 days.
2
Step 2: Set up the division: Total miles ÷ total days = miles per day, so 4160 ÷ 21.
3
Step 3: Perform the division: 21 × 198 = 4158, with a remainder of 2. Since we need whole miles, we take the quotient 198.
4
Step 4: Check reasonableness with estimation: Round 4160 to 4200 and 21 to 20. 4200 ÷ 20 = 210. Our actual answer 198 is close to 210, so it is reasonable.
Knowledge Points Involved
1
Division with Whole Numbers for Real-World Problems
Using long division to split a large whole number into equal whole-number parts, including handling remainders by rounding down when only whole units are valid (like whole miles traveled).
2
Estimation for Reasonableness Checks
Rounding numbers to simpler values to quickly calculate an approximate answer, then comparing it to the exact answer to verify that the exact result makes sense in the problem's context.
3
Unit Conversion (Weeks to Days)
Converting between units of time (weeks to days) using a known conversion factor (1 week = 7 days) to ensure consistent units for calculation.
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