Answer:
How much of a head start in miles did Mr. Smith have?
+d%5B1%5D+=+60%2A4+
+d%5B1%5D+=+240+ mi
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Start a stopwatch when Mrs. Smith leaves. Let +t+
= the time on the stopwatch in hrs when Mrs. Smith
catches up with Mr. Smith.
Let +d+ = the distance in miles that Mrs. Smith
travels until she overtakes Mr. Smith
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Mr. Smith's equation:
(1) +d+-+240+=+60t+
Mrs. Smith's equation:
(2) +d+=+80t+
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Substitute (2) into (1)
(1) +80t+-+240+=+60t+
(1) +20t+=+240+
(1) +t+=+12+
Mrs. Smith overtakes Mr. Smith in 12 hrs
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check:
(2) +d+=+80t+
(2) +d+=+80%2A12+
(2) +d+=+960+ mi
and
(1) +d+-+240+=+60t+
(1) +d+-+240+=+60%2A12+
(1) +d+=+240+%2B+720+
(1) +d+=+960+ mi