a plane flies 600 miles at a speed something then another plane flies 1000 miles at a speed +50 mph faster, ..

Question

yet takes an hour longer. What are the two planes speed.

How do I tabulate this problem. I got up to 3 and 10, but don't get it, maybe I did it wrong.

I mean I got to the part where (t-10)(t-3) so....600/3 and 1000/3?

Answer 1

OKay, let x be speed of first plane.
So, 600/x=(1000/(50+x))-1.
Or 600/x = (1000/(50+x))-((50+x)/(50+x)).
So, 600/x = ((1000-50-x)/(50+x)).
Or, 600/x = ((950-x)/(50+x)).
Cross multiplying, ((600(50+x)) = (950-x)x.
Or 30000+600x=950x-x^2.
Or, x^2-350x+30000=0.

SO, I get x=150 and x=200.
SO, it could be first plane 150, 2nd plane 200.
Or , it could be first plane 200, 2nd plane 250.

Answer 2

If you let s be the speed of the first plane, the time it took to fly 600 miles is t1 = 600 m / s. The time it took the second plane to fly 1000 miles is t2 = 1000 m / (s + 50 mph). You also have that t2 = t1 + 1 h. Putting this into an equation, you get :

1000 m / (s + 50 mph) = 600 m / s + 1 h

Multiply through by s * (s + 50 mph) to get:

s * 1000 m = (s + 50 mph) * 600 m + s * (s + 50 mph) * 1 h

With a little algebra, this can be expressed as (dropping units to keep it simple):

s^2 - 350 * s + 30,000 = 0

You can solve this equation using the quadratic formula to get

s = 150 mph or s = 200 mph.

So, one answer is that the first plane flew 600 miles in 4 hours at 150 mph and the second plane flew 1000 miles in 5 hours at 200 mph.

The other answer is that the first plane flew 600 miles in 3 hours at 200 mph and the second flew 1000 in 4 hours at 250 mph.

Answer 3

Let x be the speed of the first plane A

The time A takes is 600/x

The speed of the second plane B is x+50
therefore the time for B is 1000/(x+50)

The difference in time between the 2 plane is 1 hour
therefore the equation is

1000/(x+50) -600/x=1
multiply x(x+50) on both sides, you get
1000x-600x-30000=x^2+50x
x^2-350x+30000=0
(x-200)(x-150)=0
x=150 or 200
therefore the speed of the 2 planes are (150mph and 200mph)
or (200mph and 250mph)

Answer 4

If s = first plane's speed and t = first plane's time, then (s+50) = second plane's speed and (t+1) = its time.
600 = st
1000 = (s+50)(t+1)

solve for t in eq. 1; t = 600/s; then plug into the t in eq 2

1000 = (s+50)(600/s + 1)
Multiply out by FOIL
1000 = 600 + s + 30000/s + 50
Multiply by s to clear fractions
1000s = 600s + s^2 + 30000 + 50s
Make = 0
0 = s^2 - 350s + 30000
Factor
(s-150)(s-200) = 0
So s is 150 or 200

So 2 answers: 150 and 200 or 200 and 250

Answer 5

600 / x = 1000 / (x+50) + 1

600 = 1000 x / (x+50) + x

600x + 30000 = 1000 x + x^2 + 50x

x^2 + 450x - 30000 = 0

positive root is 58.945...

If speed were 60, first plane takes 10 hours (that's a slow plane!)

Second plane takes 1000 / 110 is about 9 hours.

UPDATE: Why the thumb down? Hayharbr gets a different answer by assuming "yet takes an hour longer" modifies the other plane, not the first plane.

Answer 6

Speed first plane = x
Speed second plane = x + 50

Time for first plane = 600/x
Time for second plane = 1000/(x+50)

1000/(x+50) - 600/x = 1

Solve for x >>
x = 200
x + 50 = 200 + 50 = 250

Another solution x = -250 is erroneous

Answer 7

600/r +1 = 1000/(r+50)
r = 200 mph = slower planes speed
r+ 50 = 250mph = faster plane's speed
600/200 = 3 hours = slower plane's time
1000/250 = 4 = faster plane's time

Answer 8

six hundred = x t, one thousand = (x+50)(t+a million), 2 equations 2 variables one thousand = x t + x.a million + 50.t + 50 one thousand = six hundred + x.a million + 50.t + 50 350 = x .a million + 50. t so x = 350 -50.t = six hundred/t rearrange and *t 50 t^2 - 350 t + six hundred = 0 simplify t^2 -7t +12= 0 sparkling up for t t= (7+/- a million)/ 2 t = 3 or 4 hours so x = 2 hundred m/h or one hundred fifty m/h verify 250*4 = one thousand and a pair of hundred* 5 =one thousand

Answer 9

Complete your question, do not use dots in your question.