Question 18597: Driver A drove 150 miles in the same amount of time that it took an airplane to travel 600 miles. The speed of the plane was 150 mph faster than the speed of the car. What is the speed of the plane. I realize the plane is 4x faster than the car but I am struggling to write the equation. please help
Answer by mmm4444bot(95)   (Show Source):
You can put this solution on YOUR website! Hello There:
I'm not sure how you decided that the plane's rate is four times faster than the car's rate. The given relationship between these two rates is that the plane moves 150 mph faster than the car.
Let's start by assigning a variable, and then an expression using that variable, for the two rates.
x = the rate of the car
x + 150 = the rate of the plane
The problem tells us that the elapsed time for each is the same, so we can write an equation using expressions for the elasped time.
Hopefully, you know the basic relationship between distance traveled, elapsed time, and rate of travel.
Distance = Rate * Time
We are dealing with time, so let's solve this equation for time by dividing each side by Rate.
Time = Distance/Rate
For the car we get 150/x.
For the plane we get 600/(x + 150)
Equating these two expressions for elapsed time gives us an equation with one variable.
150/x = 600/(x - 15)
I'll cross multiply it for you to get rid of the fractions, then you can try to solve for x on your own. Once you find x, you get the speed of the plane by adding 150.
600*x = 150*(x + 150)
~ Mark
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