SOLUTION: A commercial jet can fly from San Francisco to Dallas in three hours. A private jet can make the same trip in 3.5 hrs. If the two planes leave San Francisco at noon, after how ma

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Question 163444: A commercial jet can fly from San Francisco to Dallas in three hours. A private jet can make the same trip in 3.5 hrs. If the two planes leave San Francisco at noon, after how many hours is the private jet twice as far from Dallas as the commercial jet?
Answer by mathispowerful(115) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the number of hours, so after x hours the distance between Dallas and private jet is twice the distance between Dallas and commercial plane.
Then x%2F3 represents the portion of distance traveled by commercial airplane after x hours, 1-+x%2F3 represents the portion of total distance from Dallas to commercial air plane.
In the same way, 1+-+x%2F3.5 represent the portion of total distance between Dallas and private jet.
So we have the equation:
2%2A%281-+x%2F3%29 = 1+-+x%2F3.5
solve it:
2+-+%282x%29%2F3 = 1+-+x%2F3.5
simplify:
1 = %282x%29%2F3 - x%2F3.5
1 = %28%282x%2A3.5%29-%283%2Ax%29%29%2F%283%2A3.5%29
1 = 4x%2F10.5
x = 10.5/4 = 2.625 hrs
The answer is 2.625 hours, or 2+5%2F6 hours