Question

A passenger airplane and a private jet fly from Phoenix to Denver. It takes the jet 1.6 hours for the flight, and it takes the airplane 2.6 hours. The speed of the jet is 210 miles per hour faster than the speed of the airplane. Find the speed of both the jet and the airplane.

a) Jet speed: 420 mph, Airplane speed: 210 mph
b) Jet speed: 315 mph, Airplane speed: 105 mph
c) Jet speed: 250 mph, Airplane speed: 40 mph
d) Jet speed: 200 mph, Airplane speed: 10 mph"

Answer 1

After setting up the equation (x + 210) × 1.6 = x × 2.6 and solving for x, we find that the airplane's speed is 336 mph and the jet's speed is 546 mph. None of the given options match these speeds.

Step-by-step explanation:

To find the speeds of the jet and airplane, we can use the information given about their travel times and the speed difference. Let the speed of the airplane be x mph. Then, the speed of the jet is x + 210 mph. We know that the distance from Phoenix to Denver is the same for both the jet and airplane, so we can equate the distances they travel:

Distance = Speed × Time

For the jet: (x + 210) × 1.6

For the airplane: x × 2.6

Therefore, we can write the equation:

(x + 210) × 1.6 = x × 2.6

Solving for x:

1.6x + 336 = 2.6x

336 = 2.6x - 1.6x

336 = x

Now, we know the airplane's speed is 336 mph. The jet's speed is 336 + 210 = 546 mph. Therefore, the correct answer is not among the given choices.