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a pilot is testing a new experimental craft . the cruising speed is classified information. in a test the jet traveled 6,000 miles. the pilot reveled that if he had increased his speed 300 mph the total trip would have taken one hour less. Determine the cruising speed of the jet.

Mar 28th, 2015

Let x be the cruising speed of the jet (in mph). Then the flight took 6000/x hours. If the speed were increased by 300 mph, the flight would have taken 6000/(x+300) hours or 1 hour less.

We get an equation: 6000/x - 6000(x+300) = 1

Multiply both parts by x(x+300): 6000*(x+300) - 6000*x = x^2 + 300x

We have a quadratic equation  x^2  + 300 x - 1800000 = 0 with two solutions:

x = -150 +- sqrt{22500 + 1800000} = -150 +- sqrt{1822500} = -150 +- 1350.

Then x = 1200 mph (the second solution is -1500 < 0 and does not make sense).

Mar 28th, 2015

thank you so much this actually helped me a lot thankyou

Mar 28th, 2015

you are welcome.

Mar 28th, 2015

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