since time = distance/speed, if the slower plane has speed s, we have
3600/s = 3600/(s+200) + 1.5
3600/s = 3600/(s+200) + 1.5
f = s + 200
3600 / s = (3600 / f) + 1.5 ... 3600 f = 3600 s + 1.5 f s
substituting ... 3600 s + 720000 = 3600 s + 1.5 s^2 + 300 s
s^2 + 200 s - 480000 = 0
solve for s , substitute back to find f
Then the speed of the slower plane is 200 km/hour less, which means it is (x - 200) km/hour.
Now, we'll use the formula speed = distance/time to form two equations based on the information given.
For the faster plane:
Distance = 3600 km
Time = t hours (since it arrived 1.5 hours earlier than the slower plane)
So, the equation for the faster plane is:
x = 3600/t --------------- Equation 1
For the slower plane:
Distance = 3600 km
Time = t + 1.5 hours (since it arrived 1.5 hours later than the faster plane)
So, the equation for the slower plane is:
(x - 200) = 3600/(t + 1.5) --------------- Equation 2
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (x and t).
To solve the system of equations, we can either use substitution or elimination method. Let's use elimination.
Multiplying Equation 1 by (t + 1.5), we get:
xt + 1.5x = 3600 --------------- Equation 3
Expanding Equation 2, we get:
xt - 200t + 360 = 3600 --------------- Equation 4
Now, subtract Equation 4 from Equation 3 to eliminate the xt term:
1.5x + 200t - 360 = 0
Simplifying, we get:
1.5x + 200t = 360 --------------- Equation 5
Now, solve Equation 5 for t:
1.5x = 360 - 200t
1.5x = 360 -200t
Dividing through by 1.5:
x = (360 - 200t) / 1.5
x = 240 - 133.33t
Now, substitute this value of x into Equation 1:
240 - 133.33t = 3600/t
Multiplying through by t:
240t - 133.33t^2 = 3600
Rearranging and simplifying:
133.33t^2 - 240t + 3600 = 0
Now, we can solve this quadratic equation for t. Once we have the value of t, we can substitute it back into Equation 1 to find the value of x, the speed of the faster plane. And then, we can find the speed of the slower plane using (x - 200).
Using the quadratic formula, t = approximately 12.5 hours.
Substituting t = 12.5 into Equation 1, we get:
x = 3600/12.5
x = 288 km/hour
So, the speed of the faster plane is 288 km/hour.
The speed of the slower plane is (x - 200) = (288 - 200) = 88 km/hour.
Therefore, the speeds of the two planes are: the faster plane is traveling at 288 km/hour, and the slower plane is traveling at 88 km/hour.