1 Two planes left an airport at noon One flew east at a cert

1 Two planes left an airport at noon. One flew east at a certain speed and the other flew west twice the speed. The planes were 2700 mi (miles) apart in 3 h (hours). How fast was each plane flying?
2) Michael drove to a friend\'s house at a rate of 40 mi/h (miles per hour). He returned by the same route at a rate of 45 mi/h. The driving time for the round trip was 4 h (hours). What is the distance Michael traveled

Solution

1, Two planes left an airport at noon.
One flew east at a certain speed ;
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the other flew west twice the speed.
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The planes were 2700 mi (miles) apart in 3 h (hours).
How fast was each plane flying?
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Combined plane data:
distance = 2700 miles ; time = 3 hrs ; rate = 2700/3 = 900 mph
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1st plane rate = x
2nd plane rate = 2x
Combined plane rate = 3x mph
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EQUATION:
combines rate = combined rate
3x = 900
x = 300 mph (1st plane\'s speed)
2s = 600 mph (2nd plane\'s speed)
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2, Michael drove to a friend\'s house at a rate of 40 mi/h (miles per hour).
Outward DATA:
rate = 40 mph ; distance = x miles ; time = d/r = x/40 hrs
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He returned by the same route at a rate of 45 mi/h.
Return DATA:
rae = 45 mph ; distance = x miles ; time = d/r = x/45 hrs.
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The driving time for the round trip was 4 h (hours). What is the distance Michael traveled
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EQUATION:
time + time = 4 hrs
x/40 + x/45 = 4
85x = 4*40*45
x = 84.71 miles (distance to his friend\'s house)