two planes leave simultaneously from an airport one flying e

two planes leave simultaneously from an airport, one flying east and the other west. they are 870 mi apart after 3/4 h. if the eastbound plane averages 120 mi/h more than the westbound plane, at what rate is each plane flying?

Solution

They are going in OPPOSITE directions when miles apart is known. This means times equal, total distance given.
We also know their time.
We need to find their speed.
Let EP = eastbound plane
Let WP = westbound plane
We set up a table.
..........time..........rate.............distance
EP........3/4..........x + 120........(3/4)(x + 120)
WP........3/4.............x............(3/4)(x)
From the table we make this equation:
(3/4)(x + 120) + (3/4)(x) = the total miles they are apart or 870 miles
We now do algebra.
(3/4)(x + 120) becomes (3x/4) + 90
(3/4)(x) can be written (3x/4)
We now have a fractional equation:
(3x/4) + 90 + (3x/4) = 870
Subtracting 90 from both sides we get this:
(3x/4) + (3x/4) = 780
Let\'s add the left side fractions.
It\'s just adding fractions just like you did back in elementary school.
6x/4 = 780....This is the equation I got after adding the fractions.
To remove the fraction on the left side, multiply both sides by 4.
We are left with:
6x = 3120
To find x, divide both sides by 6.
x = 3120/6
x = 520 miles per hour.
Do you see that all that work is just algebra?
Are we done?
No! We found x but have not found their individual speed or RATE.
Eastbound plane travel at 120 mph more than the Westbound plane.
Here is your answer:
Eastbound plane = 120 + 520 or 640 miles per hour
Westbound plane is the value of x I found above or 520 miles per hour