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Two airplanes, which start 3,300 miles apart, fly toward each other. The two planes fly at a constant speed, but their speeds differ by 80 miles per hour (mph). After 5 hours, the planes pass each other. What is the speed of the faster plane?
Choose 1 answer:
(A)
290mph
(B)
338mph
(c)
370mph
(D)
450mph

Two airplanes, which start $3$ , $300$ miles apart, fly toward each other. The two planes fly at a constant speed, but their speeds differ by $80$ miles per hour (mph). After $5$ hours, the planes pass each other. What is the speed of the faster plane? $\newline$ Choose $1$ answer: $\newline$ (A) $290 \mathrm{mph}$ $\newline$ (B) $338 \mathrm{mph}$ $\newline$ (C) $370 \mathrm{mph}$ $\newline$ (D) $450 \mathrm{mph}$

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Experimental probability

Full solution

Q. Two airplanes, which start

3

,

300

miles apart, fly toward each other. The two planes fly at a constant speed, but their speeds differ by

80

miles per hour (mph). After

5

hours, the planes pass each other. What is the speed of the faster plane?

\newline

Choose

1

answer:

\newline

(A)

290 \mathrm{mph}

\newline

(B)

338 \mathrm{mph}

\newline

(C)

370 \mathrm{mph}

\newline

(D)

450 \mathrm{mph}

Denote Speeds: Let's denote the speed of the slower plane as $S$ mph and the speed of the faster plane as $S + 80$ mph. Since they are flying towards each other, their relative speed is the sum of their individual speeds.
Calculate Relative Speed: The relative speed of the two planes is $S + (S + 80)$ mph, which simplifies to $2S + 80$ mph.
Use Distance Formula: In $5$ hours, the distance covered by the two planes together at their relative speed is equal to the initial distance between them, which is $3,300$ miles. So, we can write the equation: $(2S + 80) \times 5 = 3,300$ .
Solve for S: Solving the equation for S, we get $2S + 80 = 660$ (since $3,300 / 5 = 660$ ).
Subtract $80$ : Subtracting $80$ from both sides of the equation gives us $2S = 660 - 80$ , which simplifies to $2S = 580$ .
Find Faster Plane Speed: Dividing both sides of the equation by $2$ gives us $S = \frac{580}{2}$ , which simplifies to $S = 290 \, \text{mph}$ . This is the speed of the slower plane.
Find Faster Plane Speed: Dividing both sides of the equation by $2$ gives us $S = \frac{580}{2}$ , which simplifies to $S = 290$ mph. This is the speed of the slower plane.To find the speed of the faster plane, we add $80$ mph to the speed of the slower plane: $290$ mph + $80$ mph = $370$ mph.

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