A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 15 minutes. Air traffic control approved a new flight plan that will allow her to arrive two times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.

y = 2x + 15
y equals one half times x plus 15
y equals one half times x minus 15
y = 2x − 15

y = (1/2)x + 15

Step-by-step explanation:

First, we need to identify the parts of the problem that we already know:

1) The pilot was originally scheduled to depart at 1600 (4:00 pm).

2) The pilot's departure was delayed by 15 minutes.

3) the traffic control approved a new flight plan that would allow the pilot to travel to her destination two times faster than her original flight plan.

For the problem's sake, let us pretend that the pilot's original flight plan was going to take two hours. Had he/she left at 4:00 pm, the pilot would have landed at 6:00 pm.

With a delay of 15 minutes, the duration of the flight would still remain constant, so the pilot would arrive at their destination two hours later, at 6:15 pm.

With the new flight plan, the pilot's travel time would be cut in half, so it would be 1/2 of x (time, in minutes, of original flight). Thus, her new flight time would only be one hour (60 minutes).

So, now we have to subtract 1/2 from the original flight time, as well as adding the 15 minute delay for departure. Now we can create a formula:

y = (1/2)x + 15

Y equals the total amount of time (in minutes) that it would take for the plane to leave. We divide x (total time of original flight) by 2, because her new flight plan will be twice as fast. Then we have to take into account the extra 15 minute delay!  

for the points

step-by-step explanation:

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1