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Two planes leave an airport at the same time; one flying east at
600km//hr, the other flying northwest at
400km//hr. How far apart are they after 2 hours of flying?

$4$ . Two planes leave an airport at the same time; one flying east at $600 \mathrm{~km} / \mathrm{hr}$ , the other flying northwest at $400 \mathrm{~km} / \mathrm{hr}$ . How far apart are they after $2$ hours of flying?

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Rate of travel: word problems

Full solution

Q.

4

. Two planes leave an airport at the same time; one flying east at

600 \mathrm{~km} / \mathrm{hr}

, the other flying northwest at

400 \mathrm{~km} / \mathrm{hr}

. How far apart are they after

2

hours of flying?

Calculate Distance Traveled: Calculate the distance each plane has traveled after $2$ hours. $\newline$ Distance $=$ Speed $\times$ Time $\newline$ For the eastbound plane: Distance $=$ $600$ km/hr $\times$ $2$ hr $=$ $1200$ km $\newline$ For the northwest-bound plane: Distance $=$ $=$ $0$ km/hr $\times$ $2$ hr $=$ $=$ $4$ km
Use Pythagorean Theorem: Since the planes are flying at right angles to each other, use the Pythagorean theorem to find the distance between them. $\newline$ Distance apart $^2$ = Eastbound distance $^2$ + Northwest-bound distance $^2$ $\newline$ Distance apart $^2$ = $1200$ $^2$ + $800$ $^2$ $\newline$ Distance apart $^2$ = $1440000$ + $640000$ $\newline$ Distance apart $^2$ = $2080000$
Find Distance Apart: Take the square root of the total to find the distance apart. $\newline$ Distance apart = $\sqrt{2080000}$ $\newline$ Distance apart $\approx 1442.49$ km

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