Question

Mattie Evans drove 150 miles in the same amount of time that it took a turbopropeller plane to travel 600 miles. The speed of the plane was 150 mph faster than the speed of the car. Find the speed of the plane.

Answer 1

You simply try put the whole example in an equation form.
vc= velocity of car
vp= velocity of the plane
know it is given that the time of both travels is the same, and using the famous velocity time equation you can say,
t=(distance by the car/vc)=(distance by the plane/vp)
so
(150/vc)=(600/vp)
Now, given that vp=150+vc
We have;
(150/vc)=(600/150+vc)
multiply and you get an equality of
150(150+vc)=600vc
150^2+150vc=600vc
make all vc at one side, you have;
150^2=600vc-150vc
then; vc=150^2/450=50
and use the vp=150+vc equation again and you get,
vc=200mph.
Hope this helps.

Answer 2

The speed of the plane is:

200 mph

Explanation:

Mattie Evans drove 150 miles in the same amount of time that it took a turbopropeller plane to travel 600 miles.

Let the time taken be t.

Hence, the speed of car is: 150/t

( Since, the speed is the ratio of distance traveled to the time taken )

and the speed of plane is: 600/t

Also, it is given that:

The speed of the plane was 150 mph faster than the speed of the car.

i.e.

`(600)/(t)-(150)/(t)=150\\\\i.e.\\\\(600-150)/(t)=150\\\\i.e.\\\\150t=450\\\\i.e.\\\\t=(450)/(150)\\\\i.e.\\\\t=3`

Hence, the speed of the plane is:

`=(600)/(3)\\\\=200\ mph`