Mike took a nonstop flight from New York City to Las Vegas, a total flight distance of 2,250 miles. The plan flew at a speed of 450 miles per hour for the first 90 minutes of the flight and at a speed of 440 miles per hour for the remainder of the flight. To the nearest minute, for how many minutes did the plane fly at a speed of 440 miles per hour?

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We can use the rate equation to solve this problem, but we must seperate the problem into two parts. Make sure to convert to minutes or hours accordingly.

When traveling 450 miles per hour

$$ d=rt $$ $$ d=\left(450 \frac{\text{ miles}}{\text {hr}}\right) (90 \text{ minutes}) $$ $$ d=\left(450 \frac{\text{ miles}}{\cancel{\text {hr}}}\right)(90 \cancel{\text{ minutes}})\left(\frac{1 \cancel{\text{ hr}}}{60 \cancel{\text{ minutes}}}\right) $$ $$ d=675 \text{ miles} $$

When traveling 440 miles per hour

$$ d=rt $$ $$ d= 2{,}250-675 = 1{,}575 \text{ miles} $$ $$ 1{,}575 \text{ miles}=\left(440 \frac{\text{ miles}}{\text{ hr}}\right) (t \text{ hrs}) $$ $$ t \approx 3.58 \text{ hrs or} \approx 215 \text{ minutes} $$