QuestionAn aircraft flies 1855 miles at 530 mph, using fuel at 21 lbs/min. How much fuel is used in kg?

Studdy Solution

STEP 1

Assumptions1. The conversion rate from lbs to kg is $. \mathrm{lbs}=1 \mathrm{~kg}$ . The distance from Airport A to Airport B is1855 miles3. The average speed of the aircraft is $530 \mathrm{mph}$
4. The rate of fuel consumption is $21 \mathrm{lbs} /$ minute

STEP 2

First, we need to find the flight time. We can do this by dividing the total distance by the average speed.
$Flight\, time = \frac{Total\, distance}{Average\, speed}$

STEP 3

Now, plug in the given values for the total distance and average speed to calculate the flight time.
$Flight\, time = \frac{1855\, miles}{530\, mph}$

STEP 4

Calculate the flight time.
$Flight\, time = \frac{185\, miles}{530\, mph} \approx3.\, hours$

STEP 5

We need to convert the flight time from hours to minutes, as the fuel consumption rate is given in lbs/minute. We can do this by multiplying the flight time in hours by60.
$Flight\, time =3.5\, hours \times60\, minutes/hour$

STEP 6

Calculate the flight time in minutes.
$Flight\, time =3.5\, hours \times60\, minutes/hour =210\, minutes$

STEP 7

Now that we have the flight time in minutes, we can calculate the total fuel consumption in lbs. We can do this by multiplying the flight time by the rate of fuel consumption.
$Fuel\, consumption = Flight\, time \times Fuel\, consumption\, rate$

STEP 8

Plug in the values for the flight time and the fuel consumption rate to calculate the fuel consumption in lbs.
$Fuel\, consumption =210\, minutes \times21\, lbs/minute$

STEP 9

Calculate the fuel consumption in lbs.
$Fuel\, consumption =210\, minutes \times21\, lbs/minute =441\, lbs$

STEP 10

Now that we have the fuel consumption in lbs, we can convert this to kg using the given conversion rate. We can do this by dividing the fuel consumption in lbs by the conversion rate.
$Fuel\, consumption = \frac{Fuel\, consumption\, in\, lbs}{Conversion\, rate}$

STEP 11

Plug in the values for the fuel consumption in lbs and the conversion rate to calculate the fuel consumption in kg.
$Fuel\, consumption = \frac{4410\, lbs}{.\, lbs/kg}$

STEP 12

Calculate the fuel consumption in kg.
$Fuel\, consumption = \frac{4410\, lbs}{2.2\, lbs/kg} \approx2000\, kg$ The aircraft uses approximately2000 kg of fuel during the flight.

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