SOLUTION: Julio rides his bike for 6 mi and gets a flat tire. Then he has to walk with the bike for another mile. His speed walking is 6 mph less than his speed riding the bike. If the total

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Question 603522: Julio rides his bike for 6 mi and gets a flat tire. Then he has to walk with the bike for another mile. His speed walking is 6 mph less than his speed riding the bike. If the total time is 1hr, find his speed riding the bike and his speed walking?
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(9698) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = his speed on the bike
Let +t+ = his time riding the bike
--------
Equation for riding the bike:
(1) +6+=+s%2At+
Equation walking:
(2) +1+=+%28+s+-+6+%29%2A%28+1+-+t+%29+
----------------------
(2) +1+=+s+-+6+-+s%2At+%2B+6t+
from (1):
(1) +t+=+6%2Fs+
Substitute (1) into (2)
(2) +1+=+s+-+6+-s%2A%286%2Fs%29+%2B+6%2A%286%2Fs%29+
(2) +1+=+s+-+6+-+6+%2B+36%2Fs+
Multiply both sides by +s+
(2) +s+=+s%5E2+-+12s+%2B+36+
(2) +s%5E2+-+13s+%2B+36+=+0+
Use the quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-13+
+c+=+36+
+s+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2+-+4%2A1%2A36+%29%29+%2F+%282%2A1%29+
+s+=+%28+13+%2B-+sqrt%28+169+-+144+%29%29+%2F+2+
+s+=+%28+13+%2B-+sqrt%28+25+%29%29+%2F+2+
+s+=+%28+13+%2B+5+%29%2F2+
+s+=+18%2F2+
+s+=+9+ mi/hr
and
+s+=+%28+13+-+5+%29%2F2+
+s+=+8%2F2+
+s+=+4+ ( this doesn't work, +s-6 ends up negative )
and
+s+-+6+=+9+-+6+ mi/hr
+s+-+6+=+3+ mi/hr
His speed on the bike is 9 mi/hr
His speed walking is 3 mi/hr
check:
(1) +t+=+6%2Fs+
(1) +t+=+6%2F9+ hrs
(1) +t+=+2%2F3+ hrs
and
(2) +1+=+%28+s+-+6+%29%2A%28+1+-+t+%29+
(2) +1+=+%28+9+-+6+%29%2A%28+1+-+t+%29+
(2) +1+=+3%2A%28+1+-+t+%29+
(2) +1+=+3+-+3t+
(2) +3t+=+2+
(2) +t+=+2%2F3+ hrs
OK

Answer by stanbon(57424) About Me  (Show Source):
You can put this solution on YOUR website!
Julio rides his bike for 6 mi and gets a flat tire. Then he has to walk with the bike for another mile. His speed walking is 6 mph less than his speed riding the bike. If the total time is 1hr, find his speed riding the bike and his speed walking?
------
Bike DATA:
distance = 6 miles ; rate = x mph ; time = 6/x hrs
-----
Walking DATA:
distance = 1 mile ; rate = (x-6) mph ; time = 1/(x-6) hrs
-----
Equation:
time + time = 1 hr
6/x + 1/(x-6) = 1
Multiply thru by x(x-6)
6(x-6) + x = x(x-6)
6x-36+x = x^2-6x
x^2-13x+36 = 0
---
Factor:
(x-4)(x-9) = 0
Usable solution:
x = 9 mph (bike speed)
x-6 = 3 mph (walk speed)
==========================
Cheers,
Stan H.
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