SOLUTION: Frank and Page are on opposing football teams. Frank gets the ball at his team's 20 yard line and runs for a touchdown. When Frank reaches his own 40 yd line, Page runs after him f

Algebra ->  Expressions-with-variables -> SOLUTION: Frank and Page are on opposing football teams. Frank gets the ball at his team's 20 yard line and runs for a touchdown. When Frank reaches his own 40 yd line, Page runs after him f      Log On


   

Question 628299: Frank and Page are on opposing football teams. Frank gets the ball at his team's 20 yard line and runs for a touchdown. When Frank reaches his own 40 yd line, Page runs after him from Frank's 20 yard line. Frank runs 7 yd/second, and Page runs 8 yd/second. Will Page catch up before he secures the touchdown? If so, on which yard?
~Thanks in advance~
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance in yds that Frank runs
until he gets caught by Page
Frank's equation is
(1) +d+=+7t+ where d is in yds and t is in sec
Page's equation:
(2) +d+%2B+20+=+8t+
Note that Page has to run 20 yds further and time
spent running is the same for both
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Substitute (1) into (2)
(2) +7t+%2B+20+=+8t+
(2) +t+=+20+ sec
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Now plug this back into (1) or (2)
(1) +d+=+7%2A20+
(1) +d+=+140+
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What this says is that Frank won't get caught until
he has run 140 yds. But he only needs to run 60
yds to get a TD. So Page can't stop him from scoring.