An airplane takes 4 hours to travel a distance of 2800 miles with the wind. the return trip takes 5 hours against the wind. find the speed of the plane in still air and the speed of the
wind

Speed of airplane in still air = 630 mile per hour

Speed of wind = 70 miles per hour.

Step-by-step explanation:

Let speed of plane in still air = miles/hour

Let speed of wind = miles/hour

Speed of airplane with the wind can be given by = miles/hour

Speed of airplane against the wind can be given by = miles/hour

Distance of the trip = 2800 miles

Time taken by airplane to travel with the wind = 4 hours

Speed of plane with wind =

Distance of the return trip (same trip distance) = 2800 miles

Time taken by airplane to travel with the wind = 5 hours

Speed of plane with wind =

So, we have the system of equations:

A)

B)

Using elimination method to solve.

Adding equation A to B to eliminate .

+

We get

Dividing both sides by 2.

∴

Using in equation A to find

Subtracting both sides by 630

∴

Speed of airplane in still air = 630 mile per hour

Speed of wind = 70 miles per hour.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.