Question 104935
A twin-engine plane can fly 800 mi in the same time that it takes a single-engine plane to fly 600 mi. The rate of the twin engine plane is 50 miles faster than that of the single engine plane. Find the rate of the twin engine plane.
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You got things a little mixed up here, here's how I would do it:
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Let r = speed of the twin engine plane
then
(r-50) = speed of the single engine plane
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The time of the two planes is given as the same so write a time equation:
Time = Distance/speed
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Twin time = single time
{{{800/r}}} = {{{600/(r-50))}}}
Twin:
Cross multiply and you have:
800(r-50) = 600r
:
800r - 40000 = 600r; multiplied what's inside the brackets
:
800r - 600r = +40000
200r = 40000
r = {{{40000/200}}}
r = 200 mph is the speed of the twin
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WE can check our solutions by finding if the times are the same
Single plane speed is 200 - 50 = 150 mph
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Twin: 800/200 = 4 hrs
Single: 600/150 = 4 hrs, confirms our solution:
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Did that help? I think you made it more complicated than it is: