With a tail wind a plane traveled 300 mi in 5 hours With a h

With a tail wind, a plane traveled 300 mi in 5 hours. With a head wind, the plane traveled the same distance in 8 hours. Which system of equations could be used to solve this problem? (Let s be the speed of the plane and w be the tailwind.)

Solution

velocity = distance / Time,,,,or t=d/v
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d/v1 = 5,,,,,300/(s+w) =5,,,,300=5(s+w) = 5s +5w
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d/v2 = 8,,,,,300/(s-w) =8,,,,,300 = 8(s-w) = 8s-8w
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multiply first by 8,,,and 2nd by 5
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2400=40s +40w
1500=40s-40w
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adding together
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3900 = 80s
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48.75 = s
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substituting in first eqn ,,,300 =5(48.75) +5w,,,,w=11.25
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checking, 300/ (48.75 +11.25) = 5,,,ok
300/(48.75-11.25) = 8,,,ok