angela flew a small plane for 5 hours with the wind and traveled 700km. the return trip against the wind took 7 hours. find the rate at which she flew in still air and the rate of wind
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x = rate of plane is still air
y = rate of the wind
x + y = the rate plane flies WITH the wind
x - y = the rate plane flies AGAINST the wind
D = R * T
700 = (x + y) * 5 (eqn #1)
700 = (x - y ) * 7 (eqn #2)
Simplify each:
700 = 5x + 5y (new #1)
700 = 7x - 7y (new #1)
Lots of ways to solve this system of linear equations. One thing you could do first, though, is to simplify each a little more: divide both sides of #1 by 5, and divide both sides of #2 by 7 to get:
140 = x + y (newest #1)
100 = x - y (newest #2)
Now do vertical addition on both sides to eliminate the Ys and get:
240 = 2x
120 = x = the rate of the plane in still air; substitute this into newest #1:
140 = 120 + y
20 = y = the rate of the wind
y = rate of the wind
x + y = the rate plane flies WITH the wind
x - y = the rate plane flies AGAINST the wind
D = R * T
700 = (x + y) * 5 (eqn #1)
700 = (x - y ) * 7 (eqn #2)
Simplify each:
700 = 5x + 5y (new #1)
700 = 7x - 7y (new #1)
Lots of ways to solve this system of linear equations. One thing you could do first, though, is to simplify each a little more: divide both sides of #1 by 5, and divide both sides of #2 by 7 to get:
140 = x + y (newest #1)
100 = x - y (newest #2)
Now do vertical addition on both sides to eliminate the Ys and get:
240 = 2x
120 = x = the rate of the plane in still air; substitute this into newest #1:
140 = 120 + y
20 = y = the rate of the wind