Papa drove at an average speed of 30 mph to the airport. He boarded a helicopter and travel at 60 mph to the corporate office. The entire distance was 150 miles and took 3 hours. what was he distance from the airport to the office?

Answer 1

#120# miles

I initially found this by guessing:

What if he spent an hour driving to the airport then two hours flying?

He would then travel #30# miles in the first hour and #2 xx 60 = 120# miles in the next two hours.
That all adds up since he would travel a total of #30 + 120 = 150# miles in a total of #1 + 2 = 3# hours, as required by the question.
#color(white)()# How would you calculate this without guessing?
If he spent all #3# hours driving at an average speed of #30# miles per hour, he would cover #3 xx 30 = 90# miles.
That would be #150 - 90 = 60# miles too short.
The helicopter travels an additional #60 - 30 = 30# miles per hour compared with the car.
So the helicopter portion of the journey must be #60/30 = 2# hours.
In those two hours, the helicopter travels a total of #2 xx 60 = 120# miles, which is therefore the distance between the airport and the office.
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Answer 2

Let (x) represent the distance traveled at 30 mph (from the airport to the helicopter boarding point).

Then, the remaining distance from the helicopter boarding point to the corporate office would be (150 - x) miles.

Using the formula:

[ \text{time} = \frac{\text{distance}}{\text{speed}} ]

We can set up the equation based on the given information:

[ \frac{x}{30} + \frac{150 - x}{60} = 3 ]

Solving this equation will give us the value of (x), which represents the distance from the airport to the helicopter boarding point. Then, the distance from the helicopter boarding point to the corporate office would be (150 - x).

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Answer 3

The distance from the airport to the office is 90 miles.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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