SOLUTION: Two planes left an airport at noon. One flew east at a certain speed and the other flew west at twice the speed. The planes were 2700 mi apart in 3 h. How fast was each plane flyin
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Question 94101This question is from textbook prentice hall mathematics algebra 2
: Two planes left an airport at noon. One flew east at a certain speed and the other flew west at twice the speed. The planes were 2700 mi apart in 3 h. How fast was each plane flying?
---THANKS FOR ALL YOUR HELP!!!!!!--- This question is from textbook prentice hall mathematics algebra 2
You can put this solution on YOUR website! combined mph=2700m/3h=900m/h
2x+x=900
3x=900
x=300m/h plane travelling east
2x=600m/h plane travelling west
Ed Jones
You can put this solution on YOUR website! To solve this problem use the distance formula that says the distance traveled is equal to
speed times the time.
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[Think of a car. If you go at 60 miles per hour times 2 hours, how many miles do you go???
Pretty easy to see that the answer is 120 miles which comes from 60 times 2 hrs.]
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Call the speed of one plane S. And since the other plane is going twice as fast, its speed is 2S.
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Each plane flies for 3 hours.
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The distance the first plane goes in 3 hours is its speed S times 3 hours which means it covers
a distance of 3S.
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The distance the second plane goes in 3 hours is its speed 2S times 3 hours which means
it covers a distance of 6S.
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The total distance that the planes cover is the sum of these two distances, 3S and 6S
and this equals 9S
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But the problem says the total distance between the two planes is 2700 miles.
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So we can write the equation:
.
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Then solve for S by dividing both sides of this equation by 9 to get:
.
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So one plane is going 300 miles per hour and the second plane, going twice as fast is
going 600 miles per hour.
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In 3 hours the first plane goes 300*3 = 900 miles. And in the same 3 hours the second plane
goes 600*3 = 1800 miles. This makes the total distance between the (because they are going
in opposite directions) 900 + 1800 = 2700 miles, just as the problem said it would be.
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So the answer checks out ... 300 mph and 600 mph.
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Hope this helps you see your way through the problem.
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