2017 AMC 8 Problems/Problem 23
Problem 23
Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?
Solution
We know that some multiples of go into
evenly. Let's check some because the problem specifies
minute increase.
does,
does,
does, and
does. This is
. This seems to satisfy the problem! In the first day, she travels
mile in
minutes, or
miles in
minutes. In the second day, she travels
mile in
minutes, or
miles in
minutes. In the third day, she travels
mile in
minutes, or
miles in
minutes. In the fourth day, she travels
mile in
minutes, or
miles in
minutes. Adding these up, we get
+
+
+
, which is
. So our answer is
, or
.
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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