SOLUTION: In one hour, Ed drives 25 miles farther in his car than Frank can cycle on his bike. If it takes Frank 1 1/2 hours longer to cycle 75 miles than it take Ed in his car, how fast can

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Question 435264: In one hour, Ed drives 25 miles farther in his car than Frank can cycle on his bike. If it takes Frank 1 1/2 hours longer to cycle 75 miles than it take Ed in his car, how fast can Frank cycle?
Please help me with this problem, thanks.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st sentence says that Ed's speed is 25 miles/hr
faster than Frank's
Let s = Frank's speed
Let t = Ed's time to go 75 miles in his car
Frank's equation:
+75+=+s%2A%28t+%2B+1.5%29+
Ed's equation:
+75+=+%28s+%2B+25%29%2At+
-------------------------
This is 2 equations with 2 uhnknowns,
so it's solvable
Since the distances are equal,
+s%2A%28t+%2B+1.5%29+=+%28s+%2B+25%29%2At+
+s%2At+%2B+1.5s+=+s%2At+%2B+25t+
+1.5s+=+25t+
+t+=+.06s+
+75+=+s%2A%28.06s+%2B+1.5%29+
+75+=+.06s%5E2+%2B+1.5s+
+6s%5E2+%2B+150s+-+7500+=+0+
+2s%5E2+%2B+50s+-+2500+=+0+
Using quadratic formula:
s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+2
b+=+50
c+=+-2500
s+=+%28-50+%2B-+sqrt%28+50%5E2-4%2A2%2A%28-2500%29+%29%29%2F%282%2A2%29+
s+=+%28-50+%2B-+sqrt%28+2500+%2B+20000+%29%29+%2F+4+
+s+=+%28+-50+%2B+150+%29%2F4+
+s+=+100%2F4+
+s+=+25+
Frank's speed is 25 mi/hr
check answer:
+75+=+s%2A%28t+%2B+1.5%29+
+75+=+25%2A%28t+%2B+1.5%29+
+75+=+25t+%2B+37.5+
+25t+=+37.5+
+t+=+1.5+ hr
OK
+75+=+%28s+%2B+25%29%2At+
+75+=+%2825+%2B+25%29%2At+
+75+=+50t+
+t+=+1.5+
OK