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?

1 Answer
Oct 14, 2016

#120# miles

Explanation:

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.

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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.