Question

An airplane is preparing to land at an airport. It is 36,600 feet above the ground and is descending at the rate of 3,500 feet per minute. At the same​ airport, another airplane is taking off and will ascend at the rate of 2,600 feet per minute. When will the two airplanes be at the same altitude and what will that altitude​ be?

They will be at the same altitude in

They will be at the same altitude in___ minutes when their altitude will be___feet.

Answer 1

The two airplanes will be at the same altitude after 6 minutes, and that altitude will be 15,600 feet.

Step-by-step explanation:

To determine when two airplanes will be at the same altitude, we can set up a linear equation for each airplane's altitude over time, where t represents the time in minutes after the first plane starts descending.

• The descending airplane's altitude as a function of time: A(t) = 36,600 - 3,500t
• The ascending airplane starts at the ground level: B(t) = 2,600t

We will find a common value of t where A(t) = B(t).

Setting the two equations equal to each other gives us:

36,600 - 3,500t = 2,600t

Now, combining like terms:

36,600 = 3,500t + 2,600t

36,600 = 6,100t

Dividing both sides by 6,100 gives us:

t = 6

Now that we know t, we can find the altitude at that time for either airplane:

A(6) = 36,600 - 3,500 * 6 = 36,600 - 21,000 = 15,600 feet

Therefore, they will be at 15,600 feet altitude in 6 minutes.