SOLUTION: Airplane A travels 2400 km at a certain speed. Plane B travels 1800 km at a speed 50 km/h faster than Plane A in 2 hours less time. Find the speed of each plane. Thank you

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Question 1037668: Airplane A travels 2400 km at a certain speed. Plane B travels 1800 km at a speed 50 km/h faster than Plane A in 2 hours less time. Find the speed of each plane.
Thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
            RATE       TIME      DISTANCE
A           r          t          2400
B           r+50       t-2        1800

That must make sense to you first.

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Continue when that information does make sense.


Travel Rates Rule is RT=D to relate rate, time, distance.
Form this system of equations:
system%28rt=2400%2C%28r%2B50%29%28t-2%29=1800%29
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Many algebraic steps needed in solving the system for r and t.
You would make a couple of different substitutions through the process.

Starting with the "1800" equation,
rt%2B50t-2r-100=1800
Use the first equation of the system to make substituion:
rt%2B50t-2r-100=1800
2400%2B50t-2r-100=1800
50t-2r%2B500=0
highlight_green%2825t-r%2B250=0%29
Now you will make another substitution using the "2400" equation either solved for r or solved for t...

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Airplane A travels 2400 km at a certain speed. Plane B travels 1800 km at a speed 50 km/h faster than Plane A in 2 hours less time. Find the speed of each plane.
Thank you
Let plane A’s speed be S

Then lane B’s speed is: S + 50

Time plane A takes: matrix%281%2C1%2C+%222%2C400%22%29%2FS, while plane B takes: matrix%281%2C1%2C+%221%2C800%22%29%2F%28S+%2B+50%29

We then get the following TIME equation: matrix%281%2C1%2C+%222%2C400%22%29%2FS+=+%221%2C800%22%2F%28S+%2B+50%29+%2B+2

2,400(S + 50) = 1,800S + 2S(S + 50) ------- Multiplying by LCD, S(S + 50)

2400S+%2B+2400%2850%29+=+1800S+%2B+2S%5E2+%2B+100S%29

2400S+%2B+120000+=+1900S+%2B+2S%5E2+

2S%5E2+%2B+1900S+-+2400S+-+120000+=+0

2S%5E2+-+500S+-+120000+=+0

2%28S%5E2+-+250S+-+60000%29+=+2%280%29

S%5E2+-+250S+-+60000+=+0

(S - 400)(S + 150) = 0 

S – 400 = 0		 OR		S + 150 = 0 (ignore)

S, or speed of plane A = highlight_green%28matrix%281%2C2%2C+400%2C+%22km%2Fh%22%29%29

Speed of plane B: 400 + 50, or highlight_green%28matrix%281%2C2%2C+450%2C+%22km%2Fh%22%29%29