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Difficulty: HardCalculating Distance

A military cargo plane flies for 22 hours and 2020 minutes at an average speed of 420420 miles per hour. It then encounters a strong headwind, reducing its average speed to 360360 miles per hour for the remaining 4545 minutes of the flight. What is the total distance, in miles, traveled by the cargo plane?

Answer: 1250 / 1250 miles / 1,250 / 1,250 miles

Answer

The total distance traveled by the cargo plane is 1250 miles.
The problem requires calculating the distance for two separate flight segments and adding them together. For the first segment, the time is 22 hours and 2020 minutes (73\frac{7}{3} hours) and the speed is 420420 mph, resulting in 980980 miles. For the second segment, the time is 4545 minutes (34\frac{3}{4} hours) and the speed is 360360 mph, resulting in 270270 miles. Adding these distances yields a total of 12501250 miles.

Step-by-Step Solution

1
Convert the flight time of the first leg into hours.
22 hours and 2020 minutes is equal to 2132\frac{1}{3} hours, or 73\frac{7}{3} hours.
Speed is given in miles per hour, so time must be in hours to correctly use the distance formula.
2
Calculate the distance traveled during the first leg.
420×73=980420 \times \frac{7}{3} = 980 miles.
Applying the formula Distance = Rate ×\times Time.
3
Convert the flight time of the second leg into hours.
4545 minutes is equal to 4560\frac{45}{60} hours, which simplifies to 34\frac{3}{4} hours.
Uniform units are required before calculating the distance for the second segment.
4
Calculate the distance traveled during the second leg.
360×34=270360 \times \frac{3}{4} = 270 miles.
Applying the formula Distance = Rate ×\times Time for the reduced speed segment.
5
Add the distances from both legs to find the total distance.
980+270=1250980 + 270 = 1250 miles.
The total distance is the sum of the distances traveled in each individual segment of the flight.

Key Concept

Calculating total distance for a multi-leg journey by accurately converting minutes to fractional hours and applying the Distance = Rate ×\times Time formula.
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Topics

Calculating Distance

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