<PRE><B>Question 212474</B>
flight 725 flight time is 1:06 pm minus 10:28 am.
I&#39;m assuming this is hours and minutes.
-----
Flight time for flight 725 is 2 hours and 38 minutes.
10:28 to 12:28 is 2 hours.
Another 32 minutes gets you to 1 pm.
another 6 minutes gets you to 1:06 pm.
total time is 2 hours plus 32 minutes plus 6 minutes equals 2 hours and 38 minutes.
-----
Flight time for flight 245 is 1 hour 48 minutes.
11:18 to 12:18 is 1 hour.
12:18 to 1:00 pm is 42 minutes.
1:00 pm to 1:06 pm is another 6 minutes.
total time is 1 hour plus 42 minutes plus 6 minutes equals 1 hour and 48 minutes.
-----
We need to convert these times to hours.
-----
2 hours 38 minutes is equivalent to 2.63333... hours.
1 hour 48 minutes is equivalent to 1.8 hours
-----
you take the minutes and divide them by 60 and add them to the hours to convert from hours and minutes to hours.
-----
the rate of speed for flight 725 is x (we assigned it).
-----
the rate of speed for flight 245 is 3x - 120 (it was given that flight 245 traveled 3 times as fast as flight 725 - 120 kph.  since speed of flight 725 is x kph, then speed of flight 245 is 3x - 120 kph).
-----
the basic equation to use is rate * time = distance.
-----
The distance between them is 1030 kilometers.
-----
In order to get this distance, flight 725 went north for a distance of y kilometers (unknown distance so we assign a variable to it).
-----
flight 245 went south for a distance of z kilometers (another unknown distance so we assign another variable to it.).
-----
We know that the distance of 1030 kilometers is the sum of the distance that flight 725 traveled and the distance that flight 245 traveled.
-----
We have an equation that says:
y + z = 1030
-----
This means that the distance flight 725 traveled plus the distance that flight 245 traveled equals 1030 kilometers.
-----
We know that flight 725 traveled y kilometers.
We also know that flight 725 traveled at x kilometers per hour.
We also know that flight 725 traveled for 2.63333... hours.
-----
This tells us that flight 725 traveled y kilometers and that y = 2.63333... * x
because rate * time = distance and:
distance = y
time = 2.6333... hours
rate = x kilometers per hour.
-----
We know that flight 245 traveled z kilometers.
We also know that flight 245 traveled at (3x-120) kilometers per hour.
We also know that flight 245 traveled for 1.8 hours.
-----
This tells us that flight 245 traveled z kilometers and that z = 1.8 * (3x-120) because rate *&amp; time = distance and:
distance = z
time = 1.8 hours
rate = (3x-120) kilometers per hour.
-----
We started off with an equation that says:
y + z = 1030
We know that:
y = 2.63333... * x
We also know that:
z = 1.8 * (3x-120)
-----
Our equation:
y + z = 1030
becomes:
2.63333... * x + 1.8 * (3x-120) = 1030
-----
Now we have one equation in one unknown and we can solve for x.
-----
expanding the equation by removing the parentheses, we get:
(2.6333... * x) + (1.8 * 3x) - (1.8 * 120) = 1030 
this becomes:
(2.6333... * x) + (5.4 * x) - 216 = 1030 
combine like terms to get:
8.0333... * x = 1030 + 216
this becomes:
8.0333... * x = 1246
-----
divide both sides of this equation by 8.0333... to get:
x = 155.1037344
-----
if x = 155.1037344 kph, then:
3x - 120 = 345.3112033 kph.
-----
We have enough now to figure out the kilometers.
flight 725 traveled for 2.6333... hours at 155.1037344 kph to make a distance of 408.439834 kilometers.
-----
flight 245 traveled for 1.8 hours at 345.3112033 kph to make a distance of 621.560166 kilometers.
-----
sum of these kilometers is 408.439834 + 621.560166 = 1030 so we have the right rates of travel.
-----
answer to the question is:
rate of speed of flight 725 is 155.1037344 kph and rate of speed of flight 245 is 345.3112033 kph.
-----
</PRE>