SOLUTION: While riding a bicycle one afternoon, Pete discovered that he could travel 15 miles while riding with a 6 mile per hour tailwind in the same amount of time that it took to travel 9

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Question 1007320: While riding a bicycle one afternoon, Pete discovered that he could travel 15 miles while riding with a 6 mile per hour tailwind in the same amount of time that it took to travel 9 miles into the same wind. At what rate could Pete ride with no wind at all?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = his speed with no wind
+s+%2B+6+ = his speed riding with the wind
+s+-+6+ = his speed riding into the wind
Let +t+ = his time in hrs riding both ways
-------------------------------------
Riding with the wind:
(1) +15+=+%28+s+%2B+6+%29%2At+
Riding against the wind:
(2) +9+=+%28+s+-+6+%29%2At+
--------------------
(1) +t+=+15%2F%28+s+%2B+6+%29+
Substitute this result into (2)
(2) +9+=+%28+s+-+6+%29%2A%28+15%2F%28+s+%2B+6+%29%29+
Multiply both sides by +s+%2B+6+
(2) +9%2A%28+s+%2B+6+%29+=+15%2A%28+s+-+6+%29+
(2) +9s+%2B+54+=+15s+-+90+
(2) +6s+=+144+
(2) +s+=+24+
His speed with no wind is 24 mi/hr
----------------
check:
(1) +15+=+%28+s+%2B+6+%29%2At+
(1) +15+=+%28+24+%2B+6+%29%2At+
(1) +15+=+30t+
(1) +t+=+1%2F2+
and
(2) +9+=+%28+s+-+6+%29%2At+
(2) +9+=+%28+24+-+6+%29%2At+
(2) +9+=+18t+
(2) +t+=+1%2F2+
OK