SOLUTION: Mattie Evans drove 200 miles in the same amount of time that it took a turbo propeller plane to travel 920 miles. The speed of the plane was 180 mph faster than the speed of the

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Question 1161706: Mattie Evans drove 200 miles in the same amount of time that it took a turbo propeller plane to travel 920 miles. The speed of the plane was 180
mph faster than the speed of the car. Find the speed of the plane.
Found 4 solutions by josgarithmetic, jim_thompson5910, MathTherapy, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
R, speed
T, time
D, distance
R=D%2FT
1%2FR=T%2FD
highlight_green%28T=D%2FR%29

If r is speed of plane, then description means car speed r-180.

If both traveled same amount of time, then highlight_green%28200%2F%28r-180%29=920%2Fr%29. Solve for r.

--

10%2F%28r-180%29=46%2Fr
5%2F%28r-180%29=23%2Fr
23%28r-180%29=5r
23r-23%2A180=5r
18r-23%2A180=0
18r=23%2A18%2A10
highlight%28r=230%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Here is the distance-rate-time table for both the car and plane
DistanceRate or SpeedTime
Car200200/tt
Plane920920/tt

You start off filling out the distances for each. Those are the given numeric values. The time t is the same for both the car and plane. The rate or speed is found using the formula r = d/t, which comes from d = r*t. The table is optional, but may be handy to keep track of everything.

We know that the plane goes 180 mph faster than the car, so this means
plane's speed = (car's speed) + 180
920/t = (200/t) + 180
920 = 200 + 180t
on the last step, I multiplied every term by t to clear out the fractions

From here, let's solve for t
920 = 200 + 180t
920-200 = 180t
720 = 180t
180t = 720
t = 720/180
t = 4

Both car and plane travel for t = 4 hours.
Doing so, the car's speed is r = d/t = 200/4 = 50 mph
and the plane's speed is r = d/t = 920/4 = 230 mph
The plane's speed is 230-50 = 180 mph greater than that of the car

Answer: plane's speed = 230 mph

Answer by MathTherapy(10557) About Me  (Show Source):
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Mattie Evans drove 200 miles in the same amount of time that it took a turbo propeller plane to travel 920 miles. The speed of the plane was 180
mph faster than the speed of the car. Find the speed of the plane.
Let plane's speed be S

Then Mattie's vehicle's speed = S - 180

We then get the following TIME equation: matrix%281%2C3%2C+920%2FS%2C+%22=%22%2C+200%2F%28S+-+180%29%29

matrix%281%2C3%2C+23%2FS%2C+%22=%22%2C+5%2F%28S+-+180%29%29 ------ Factoring out GCF, 40, in numerator

23(S - 180) = 5S ---- Cross-multiplying 

23S - 23(180) = 5S

23S - 5S = 23(180)

18S = 23(180)

Plane's speed, or

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Solving an equation to find the answer -- as shown by several other tutors -- is certainly a valid approach to the problem....

But there is a much easier path to the answer.

The difference in distances was 720 miles; the difference in speed was 180mph.
That means the time was 720/180 = 4 hours.
That means the plane's speed was 920/4 = 230mph.