Question 66725
1- a six passanger 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?
With Wind:
rate = 180 + x
time = t
distance = 7
distance/rate = time
With Wind: 7/(180 + x) = t
Against Wind:
rate = 180 - x
time = t
distance = 5
distance/rate = time
Against Wind: 5/(180 - x) = t
t = t
7/(180 + x) = 5/(180 - x)
7(180 - x) = 5(180 + x)
1260 - 7x = 900 + 5x
360 = 12x
30 = x
The wind was 30mph.
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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 longer than Smith's. How fast was each one traveling ?
Smith:
rate = r
time = t
distance = 45
distance/time = rate
45/t = r
Jone:
rate = r + 5
time = t + 1.5
distance = 70
distance/time = rate
70/(t + 1.5) = r + 5
70/(t + 1.5) - 5 = r
r = r
45/t = 70/(t + 1.5) - 5
{{{graph(300,300,-8,8,-10,28,45/x,70/(x + 1.5) - 5)}}}