Question 66725
1- a six passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind. in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?
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Let x = wind speed:
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Speed against the wind = (180-x)
Speed with the wind = (180+x)
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Write a time equation: time = dist/speed
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{{{5/((180-x))}}} = {{{7/((180+x))}}}
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Cross multiply and you have:
5(180+x) = 7(180-x)
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900 + 5x = 1260 - 7x
5x + 7x = 1260 - 900
12x = 360
x = 360-12
x = 30 mph speed of the wind:
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Check: 5/150 = 7/210
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2- Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour than Smith's. How fast was each one traveling ?
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I understand this to mean: 
Jones' 70 mi trip took a half hr longer than Smith's 45 mi trip
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Let Smith's speed = s
Then Jones' speed = (s+5)
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Write a time equation again:
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Smith's time + .5 hr = Jones' time
{{{45/s + 1/2}}} = {{{70/((s+5))}}}
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Get rid of the denominators by multiplying equation by 2s(s+5), you then have:
45(2(s+5)) + s(s+5) = 70(2s)
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90s +  450 + s^2 + 5s = 140s
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s^2 + 90s + 5s - 140s + 450 = 0
:
s^2 - 45s + 450 = 0
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This quadratic equation will factor to:
(s-30)(s-15) = 0
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s = 30 mph or s = 15 mph
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Both solutions will work, however, practically the bike av speed would be:
Smith: 15 mph and Jones: 20 mph, I would think
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Check:
Jones time - Smiths time
70/20 - 45/15 =
 3.5 hr - 3 hr = 1/2 hr