SOLUTION: Jane's work commute is 6 miles. When the roads are icy, she travels 20mph slower and takes 9 minutes (or 3/20 hours) longer to get to work. How long does it take her to get to work

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Question 685815: Jane's work commute is 6 miles. When the roads are icy, she travels 20mph slower and takes 9 minutes (or 3/20 hours) longer to get to work. How long does it take her to get to work when the roads are icy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need 2 equations, one for regular commute
and one for icy roads
Let +s+ = her regular speed in mi/hr
Let +t+ = her regular time in hrs
------------
given:
For regular commute:
(1) +6+=+s%2At+
For icy roads:
(2) +6+=+%28+s+-+20+%29%2A%28+t+%2B+3%2F20+%29+
-----------------------------
(2) +6+=+s%2At+-+20t+%2B+%283%2F20%29%2As+-+3+
Make these substitutions:
(1) +s%2At+=+6+
and
(1) +s+=+6%2Ft+
--------------
(2) +6+=+6+-+20t+%2B+%283%2F20%29%2A%286%2Ft%29+-+3+
(2) +3+=+-20t+%2B+%28+9%2F10t+%29+
Multiply both sides by +10t+
(2) +30t+=+-200t%5E2+%2B+9+
(2) +200t%5E2+%2B+30t+-+9+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+200+
+b+=+30+
+c+=+-9+
+t+=+%28-30+%2B-+sqrt%28+30%5E2+-+4%2A200%2A%28-9%29+%29%29+%2F+%282%2A200%29+
+t+=+%28-30+%2B-+sqrt%28+900+%2B+7200+%29%29+%2F+400+
+t+=+%28-30+%2B-+sqrt%28+8100+%29%29+%2F+400+
+t+=+%28+-30+%2B+90+%29+%2F+400+ ( ignore the negative square root )
+t+=+60+%2F+400+
+t+=+.15+ hrs
+.15%2A60+=+9+ min
When roads are icy,
+t+%2B+9+=+9+%2B+9+
+t+%2B+9+=+18+
When roads are icy, it takes 18 minutes
check:
(1) +6+=+s%2At+
(1) +6+=+s%2A.15+
(1) +s+=+40+
and
(2) +6+=+%28+s+-+20+%29%2A%28+t+%2B+3%2F20+%29+
(2) +6+=+%28+40+-+20+%29%2A%28+.15+%2B+.15+%29+
(2) +6+=+20+%2A+.3+
(2) +6+=+6+
OK