SOLUTION: Each Saturday, Sarah and Beccy drive from the town of Littlesburgh to the city of Bigsford to go shopping. The last time they made the journey, Sarah set off at 8:15 am, travelling

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Question 819351: Each Saturday, Sarah and Beccy drive from the town of Littlesburgh to the city of Bigsford to go shopping. The last time they made the journey, Sarah set off at 8:15 am, travelling at 30mph. Beccy set off at 8:27 am but was travelling at 50mph.

Assuming they remain at these speeds and do not stop, at what time does Beccy overtake Sarah, and how far away were they both from Littlesburgh?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How much of a head start did Sarah get?
+d%5B1%5D+=+30%2A%2812%2F60%29+=+6+ miles
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Start a stopwatch when Becky leaves
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Let +d+ = the distance that Becky travels
until she catches Sarah.
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Let +t+ = the time on the stopwatch when
Becky catches Sarah.
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Equation for Sarah:
(1) +d+-+6+=+30t+
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Equation for Becky:
(2) +d+=+50t+
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Substitute (2) into (1)
(1) +50t+-+6+=+30t+
(1) +20t+=+6+
(1) +t+=+3%2F10+ hrs
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+%283%2F10%29%2A60+=+18+ min
Becky overtakes Sarah at 8:27 + 18 min = 8:45
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(2) +d+=+50t+
(2) +d+=+50%2A%283%2F10%29+
(2) +d+=+15+
They are 15 miles from Littlesburgh
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check:
(1) +d+-+6+=+30t+
(1) +15+-+6+=+30%2A%283%2F10%29+
(1) +9+=+9+
OK