SOLUTION: Mattie Evans drove 250 miles in the same amount of time that it took a turbo propeller plane to travel 1200 miles. The speed of the plane was 190 mph faster than the speed of the c

Question 1162431: Mattie Evans drove 250 miles in the same amount of time that it took a turbo propeller plane to travel 1200 miles. The speed of the plane was 190 mph faster than the speed of the car. Find the speed of the plane.
The speed of the plane was _ mph.
Found 5 solutions by Theo, josgarithmetic, MathTherapy, greenestamps, Alan3354:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
rate * time = distance.
let x equal the rate that mattie travels at.
let y equal the rate that the plane travels at.
let z = the time
for the car, the formula becomes x * z = 250
for the plane, the formula becomes y * z = 1200
you are given that the rate of the plane is 190 miles per hour faster than the rate of the car.
this means y = x + 190
the formulas become:
x * z = 250
(x + 190) * z = 120
simplify the second equation and leave the first equation as is to get:
x * z = 250
x * z + 190 * z = 1200
subtract the first equation from the second to get:
190 * z = 950
solve for z to get:
z = 5
that's the time the the car and the plane took.
for the car, x * z = 250 becomes x * 5 = 250.
solve for x to get x = 50 miles per hour.
y = x + 190 makes y = 240 miles per hour.
for the car, the formula becomes:
5 * 50 = 250 miles
for the plane, the formula becomes:
5 * 240 = 1200 miles
solution looks good.
solution is that the speed of the plane is 240 miles per hour.
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Let p be the speed of the plane.
The speed Mattie drove was p-190.

----------simplify and solve for p.
Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!
Mattie Evans drove 250 miles in the same amount of time that it took a turbo propeller plane to travel 1200 miles. The speed of the plane was 190 mph faster than the speed of the car. Find the speed of the plane.
The speed of the plane was _ mph.

Let plane's speed be S
Then car's speed = S - 190.
Plane's and car's times: , respectively
As their times are the same, we get the following DISTANCE equation:
------- Factoring out GCF, 50, in numerator
5S = 24(S - 190) ----- Cross-multiplying
5S = 24S - 24(190)
5S - 24S = - 24(190)
- 19S = - 24(190)
Plane's speed, or
The other person, as usual, gave you a very complex and time-consuming solution, but it doesn't have to be that way.
It's much SIMPLER than the way he presents it. Unless of course, you prefer complex and much time-consuming solutions, or understand them better.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The solution is quick and easy, if a formal algebraic solution is not required.

The difference in distances is 950 miles; the difference in speeds is 190mph. That means the time was 950/190 = 5 hours.

So the speed of the plane was 1200/5 = 240mph (and the speed of the car was 250/5 = 50mph).

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The speed of the plane was 190 mph faster than the speed of the car.
================
The speed of the plane was not 190 mph faster.
Speeds do not travel.
-----
The plane was 190 mph faster, or
The speed of the plane was 190 mph greater than the speed of the car.
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