Problem Solving Skills for Mathcounts Competitions
Book Store => Bookstore => Twenty Mock Mathcounts Sprint Round Practices => Topic started by: yongcheng3315 on March 17, 2012, 07:18:05 PM
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Test 19 corrections
(1)
Question 8: It takes Alex 15 minutes to catch Betsy the first time and to run a total of 16 rounds more..." means
Alex uses 15 minutes to catch Betsy the first time. When he catches Betsy the first time, Betsy runs x rounds and he runs (16 + x) rounds.
(2)
Test 19 #5
Should read AC = m
D is not labeled on diagram
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#8 Solution:
Method 1:
Let d be the circumference of the circle and x be the number of rounds Betsy runs:
(25/60)[(16+x)d/15 + xd/15] = d
Solve for x: x = 10.
Method 2:
Let Va and Vb be the speeds of Alex and Betsy, respectively.
(25/60)(Va + Vb) = d (1)
15(Va - Vb) = 16d (2)
Solve for Va/Vb.
Then Va/Vb = (16+x)/x.
x = 10.