Question 174710
If Bill rides his bike 3 mi to Fred's house and then walks with Fred the remaining 1 mi to school, it will take him 30 min. But if he rides the entire distance, it will take him only 20 min. Find his biking speed and walking speed. 
for this equation, i tried to set the problems up like this: 
3 b + 1 w= 30 min
b = 20 min 
3(20) + 1 w = 30 
60 + 1 w = 30
-60 -60
1 w = -30
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Bill DATA:
Bike:
distance = 3 mi ; rate =  b mph ; time = d/r = 3/b hrs
Walk:
distance = 1 mi : rate = w mph ; time = d/r = 1/w hrs
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Bill equation: 
time + time = (1/2) hr
(3/b) + (1/w) = 1/2
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Bill DATA:
distance = 4 mi; rate = b mph ; time = 4/b hrs
Bill/bike equation: 
4/b = (1/3) hr
b/4 = 3
b = 12 mph (speed at which Bill bikes)
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Substitute into (3/b) + (1/w) = 1/2 to solve for "w"
3/12 +  1/w = 1/2
1/w = 1/4
w = 4 mph (speed at which Bill walks)
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Cheers,
Stan H.