Question 116080
At 7:00 a.m. Joe starts jogging at 6 mph. At 7:10 a.m. Ken starts off after him. How fast must Ken run in order to overtake him at 7:30 a.m.
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Since we are dealing in mph,
Change J's run time to hrs, 30 min = {{{1/2}}} hr
Change K's run time to hrs, 20 min = {{{1/3}}}hr
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Let s = Ken's speed (mph) to overtake Joe at 7:30
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When K overtakes J they will have traveled the same distance
Write a distance equation: Dist = time * speed
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K's dist = J's dist
{{{1/3}}}s = {{{1/2}}}(6)
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Cross multiply:
2s = 3(6)
s = {{{18/2}}}
s = 9 mph for K to catch up with J at 7:30
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Check solution by finding that their distances are, indeed, equal:
{{{1/2}}}(6) = 3 mi
{{{1/3}}}(9) = 3 mi