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Zorluk: OrtaCalculating Distance

A military cargo plane flies from Base Alpha to Base Bravo at a steady cruising speed of 320 miles per hour320\text{ miles per hour}. This first leg of the flight takes 2 hours and 45 minutes2\text{ hours and } 45\text{ minutes}. After refueling, the plane continues to Base Charlie, flying at 280 miles per hour280\text{ miles per hour} for 1 hour and 30 minutes1\text{ hour and } 30\text{ minutes}. What is the total distance traveled by the cargo plane from Base Alpha to Base Charlie? Include both the numeric value and unit in your answer (e.g., '500 miles').

Cevap: 1300 miles / 1,300 miles / 1300 mi / 1300 / 1,300

Cevap

1300 miles
The correct answer is found by first converting all travel times into decimal hours. The first leg is 2.752.75 hours at 320 mph320\text{ mph}, covering 880 miles880\text{ miles}. The second leg is 1.51.5 hours at 280 mph280\text{ mph}, covering 420 miles420\text{ miles}. Adding these two distances yields a total of 1300 miles1300\text{ miles}.

Adım Adım Çözüm

1
Convert the flight times into decimal hours.
2 hours and 45 minutes=2.75 hours2\text{ hours and } 45\text{ minutes} = 2.75\text{ hours}; 1 hour and 30 minutes=1.5 hours1\text{ hour and } 30\text{ minutes} = 1.5\text{ hours}.
To calculate distance using miles per hour, the time units must be converted to hours.
2
Calculate the distance for the first leg from Base Alpha to Base Bravo.
320 mph×2.75 hours=880 miles320\text{ mph} \times 2.75\text{ hours} = 880\text{ miles}.
Distance equals rate multiplied by time (d=r×td = r \times t).
3
Calculate the distance for the second leg from Base Bravo to Base Charlie.
280 mph×1.5 hours=420 miles280\text{ mph} \times 1.5\text{ hours} = 420\text{ miles}.
The second leg must be calculated independently due to the change in both speed and travel time.
4
Add the distances of both legs to find the total distance traveled.
880 miles+420 miles=1300 miles880\text{ miles} + 420\text{ miles} = 1300\text{ miles}.
The total journey distance is the sum of the distances of all individual legs.

Anahtar Kavram

Calculating multi-leg total distance using d=r×td = r \times t with unit conversions.
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