SOLUTION: Erin rides her bike from home to school in 15 minutes. If she increases her speed by 5 km/hr, she reduces her travel time by 5 minutes. What is the distance from her home to her

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Question 1085265: Erin rides her bike from home to school in 15 minutes. If she increases her speed by 5 km/hr, she reduces her travel time by 5 minutes. What is the distance from her home to her school.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance from home to school in km
Let +s+ = her speed in km/hr
Let +t+ =her time in hrs to go from home to school
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+d+=+s%2At+
Convert minutes to hrs
[ min ] x [ hrs/min ] = [ hrs ]
+15%2A%28+1%2F60+%29+=+1%2F4+ hrs
and, also:
+5%2A%281%2F60%29+=+1%2F12+ hrs
----------------------------
Her equation for a normal trip is:
(1) +d+=+s%2A%281%2F4%29+
If she increases her speed, the equation is:
(2) +d+=+%28+s+%2B+5+%29%2A%28+1%2F4+-+1%2F12+%29+
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(2) +d+=+%28+s+%2B+5+%29%2A%28+2%2F12+%29+
(2) +d+=+%28+s+%2B+5+%29%2A%281%2F6%29+
Plug (1) into (2)
(2) +%281%2F4%29%2As+=+%28+s+%2B+5+%29%2A%281%2F6+%29+
Multiply both sides by +12+
(2) +3s+=+2%2A%28+s+%2B+5+%29+
(2) +3s+=+2s+%2B+10+%7D%7D%0D%0A%282%29+%7B%7B%7B+s+=+10+ km/hr
and
(1) +d+=+s%2A%281%2F4%29+
(1) +d+=+10%2A%281%2F4%29+
(1) +d+=+2.5+ km
The distance from home to school is 2.5 km
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check answer:
(2) +d+=+%28+s+%2B+5+%29%2A%281%2F6%29+
(2) +d+=+%28+10+%2B+5+%29%2A%281%2F6%29+
(2) +d+=+15%2F6+
(2) +d+=+5%2F2+
(2) +d+=+2.5+ km
OK