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Calculate Airplane Flight Distance in 1 Hour Given 104 Miles in 50 Minutes
Mathematics
Grade 6
Question Content
A small airplane flew 104 miles in 50 minutes. At this rate, how many miles can it fly in one hour? (50 minutes = 5/6 hour)
Correct Answer
124.8 miles
Detailed Solution Steps
1
Step 1: Use the given converted time: 50 minutes = 5/6 hour.
2
Step 2: Calculate the constant speed of the airplane using speed = distance ÷ time. Speed = 104 miles ÷ (5/6) hour = 104 × (6/5) = 124.8 miles per hour.
3
Step 3: Multiply the speed by 1 hour to find the distance in one hour: 124.8 miles/hour × 1 hour = 124.8 miles.
Knowledge Points Involved
1
Fractional Unit Conversion
This involves representing minutes as a fraction of an hour (e.g., 50 minutes = 5/6 hour) instead of a decimal. It is useful for precise calculations with non-whole number time values in rate problems.
2
Dividing by a Fraction
Dividing a number by a fraction is equivalent to multiplying the number by the reciprocal of the fraction (a ÷ (b/c) = a × (c/b)). This rule is used to calculate speed when time is given as a fractional value of an hour.
3
Constant Rate Motion
This assumes the speed of an object remains unchanged for the entire travel period. It allows us to use the calculated speed to predict distance traveled for any given time, as long as the rate stays consistent.
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