SOLUTION: Lia walks to the mall from her house at 5mph. 10 minutes later, Lia's sister Megan starts to ride her bike from the same house at 15mph to the mall to meet Lia. They arrive at the

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Lia walks to the mall from her house at 5mph. 10 minutes later, Lia's sister Megan starts to ride her bike from the same house at 15mph to the mall to meet Lia. They arrive at the       Log On

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Question 1103664: Lia walks to the mall from her house at 5mph. 10 minutes later, Lia's sister Megan starts to ride her bike from the same house at 15mph to the mall to meet Lia. They arrive at the same time. How far is the mall from the sister's house? How long did it take Megan to get there?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance from mall to house
Let +t+ = time in hrs for them both
to arrive at the mall
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What is Lisa's head start in miles ?
Also, convert 10 min to hrs
+10%2F60+=+1%2F6+ hrs
+d%5B1%5D+=+5%2A%281%2F6%29+
+d%5B1%5D+=+5%2F6+ mi
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Start a stop watch when Megan leaves the house
+t+ will be the time on the stop watch when
they both arrive at mall
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Megan's equation:
(1) +d+=+15t+
Lia's equation:
(2) +d+-+5%2F6+=+5t+
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Plug (1) into (2)
(2) +15t+-+5%2F6+=+5t+
(2) +10t+=+5%2F6+
(2) +t+=+5%2F60+ hrs
convert hrs to min:
(2) +%285%2F60%29%2A60+=+5+
It takes Megan 5 min to get to mall
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(1) +d+=+15t+
(1) +d+=+15%2A%285%2F60%29+
(1) +d+=+75%2F60+
(1) +d+=+1.25+
It is 1.25 miles from house to mall
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check:
(2) +d+-+5%2F6+=+5t+
(2) +d+-+5%2F6+=+5%2A%285%2F60%29+
(2) +d+=+25%2F60+%2B+50%2F60+
(2) +d+=+75%2F60+
(2) +d+=+1.25+
OK