SOLUTION: Pat biked 1 mile in 3 minutes with the wind at her back, and then she returned in 4 minutes riding against the wind. What was the speed of wind?

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Question 558016: Pat biked 1 mile in 3 minutes with the wind at her back, and then she returned in 4 minutes riding against the wind. What was the speed of wind?
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Pat biked 1 mile in 3 minutes with the wind at her back, and then she returned in 4 minutes riding against the wind. What was the speed of wind?
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There's no simple or well-defined relation between wind speed and bike speed.
You ever ridden a bike?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed with no wind
Let +w+ = the wind speed
+s+%2B+w+ = biking speed with the wind
+s+-+w+ = biking speed against the wind
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given:
(1) +1+=+%28+s+%2B+w+%29%2A3+
(2) +1+=+%28+s+-+w+%29%2A4+
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(1) +1+=+3s+%2B+3w+
(2) +1+=+4s+-+4w+
Multiply both sides of (1) by 4
and both sides of (2) by 3
Then add the equations
(1) +4+=+12s+%2B+12w+
(2) +3+=+12s+-+12w+
+7+=+24s+
+s+=+7%2F24+ mi/min
+7%2F24+ mi/min x +60+ min/mi = +17.5+ mi/hr
and
(1) +1+=+3s+%2B+3w+
(1) +1+=+3%2A%287%2F24%29+%2B+3w+
(1) +3w+=+24%2F24+-+21%2F24+
(1) +3w+=+3%2F24+
(1) +w+=+1%2F24+ mi/min
+1%2F24+ mi/min x +60+ min/hr = +2.5+ mi/hr
The wind speed was 2.5 mi/hr
check answer:
(1) +1+=+%28+s+%2B+w+%29%2A%283%2F60%29+ (note that 3 min = +3%2F60+ hrs)
(1) +1+=+%28+17.5+%2B+2.5+%29%2A%283%2F60%29+
(1) +1+=++20%2A%283%2F60%29+
(1) +1+=+60%2F60+
(1) +1+=+1+
and
(2) +1+=+%28+s+-+w+%29%2A%284%2F60%29+
(2) +1+=+%28+17.5+-+2.5+%29%2A%284%2F60%29+
(2) +1+=+15%2A%284%2F60%29+
(2) +1+=+60%2F60+
(2) +1=+1+
'OK