Mattie Evans drove 250 miles in the same amount of time that it took a turbo propeller plane to travel 1250 miles. The speed of the plane was 200 mph faster than the speed of the car. Find the speed of the plane.

250 mph

Step-by-step explanation:

Speed of car = Distance / Time =

The speed of the plane was 200 mph faster than the speed of the car.

Speed of car = X mph

Speed of plane = 200 + X mph

Evans drove 250 miles in the same amount of time...

Speed = Distance / Time

Time = Distance / Speed

T = 250 / X (i)

same amount of time that it took a turbo propeller plane to travel 1250 miles.

Time = Distance / Speed

T = 1250 / (200 + X) (ii)

Substitute the value of T in eqn (i) to eqn (ii)

250 / X = 1250 / (250 + X)

250 (200 + X) = 1250 X

50000 + 250 X = 1250 X

1250 X - 250 X = 50000

1000X = 50000

X = 50000 / 1000 = 50

Speed of plane = 200 + X mph = 200 + 50 = 250 mph

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!