SOLUTION: 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 le

Question 158175This question is from textbook Algebra and Trigonometry: Structure and Method, book 2
: 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? This question is from textbook Algebra and Trigonometry: Structure and Method, book 2

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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?
.
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
.
Let x = average speed of second part of race
.
Time for first part of race:
20/16
.
Time for second part of race:
30/x
.
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
.
Conclusion: he has to average greater than 24 mph

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