Question 158175
    During the first 20 mi of a 50mi bicycle race, Toger's average speed was 16 mi/h. Must must his average speed be during the remainder of the race if he is to finish the race in less than 2.5 hours?
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You must apply the "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
However, since the problem is focused on "time", let's solve for 't':
d = rt
dividing both sides by r:
d/r = t
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Let x = average speed of second part of race
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Time for first part of race:
20/16 
.
Time for second part of race:
30/x 
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Total time should equal "less than" 2.5:
20/16 + 30/x < 2.5
Multiplying both sides by 16x:
16x[20/16 + 30/x] < 16x[2.5]
20x + 480 < 40x
480 < 20x
24 mph < x
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Conclusion: he has to average greater than 24 mph