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Along a straight coastal road, four stops, Harbor, Maple, Ridge, and Summit, appear in that order. Ridge is 3 times as far from Harbor as it is from Summit. Maple is 4 times as far from Ridge as it is from Harbor. What fraction of the distance from Harbor to Summit is the distance from Maple to Summit?
A. \(\frac{3}{20}\)
B. \(\frac{1}{4}\)
C. \(\frac{2}{5}\)
D. \(\frac{17}{20}\)
E. \(\frac{20}{17}\)
A. \(\frac{3}{20}\)
B. \(\frac{1}{4}\)
C. \(\frac{2}{5}\)
D. \(\frac{17}{20}\)
E. \(\frac{20}{17}\)
07 Aug 2026, 03:46
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Official Solution:
Along a straight coastal road, four stops, Harbor, Maple, Ridge, and Summit, appear in that order. Ridge is 3 times as far from Harbor as it is from Summit. Maple is 4 times as far from Ridge as it is from Harbor. What fraction of the distance from Harbor to Summit is the distance from Maple to Summit?
A. \(\frac{3}{20}\)
B. \(\frac{1}{4}\)
C. \(\frac{2}{5}\)
D. \(\frac{17}{20}\)
E. \(\frac{20}{17}\)
The stops are in this order:
\(H --- M ------------ R ----- S\)
\(H\) = Harbor, \(M\) = Maple, \(R\) = Ridge, \(S\) = Summit
Since Ridge is 3 times as far from Harbor as it is from Summit:
\(HR : RS = 3:1\)
So \(HR = \frac{3}{4}\) of \(HS\).
Since Maple is 4 times as far from Ridge as it is from Harbor:
\(MR : HM = 4:1\)
So \(HM = \frac{1}{5}\) of \(HR\).
Choose \(HS = 20\), since 20 is the least common multiple of 4 and 5.
Then:
\(HR = \frac{3}{4} * 20 = 15\)
\(RS = 5\)
And:
\(HM = \frac{1}{5} * 15 = 3\)
\(MR = 12\)
So the diagram is:
\(H -(3)-- M ------(12)------ R --(5)--- S\)
The distance from Maple to Summit is:
\(MS = MR + RS = 12 + 5 = 17\)
The full distance from Harbor to Summit is:
\(HS = 20\)
Therefore, the required fraction is:
\(\frac{17}{20}\)
Answer: D
Along a straight coastal road, four stops, Harbor, Maple, Ridge, and Summit, appear in that order. Ridge is 3 times as far from Harbor as it is from Summit. Maple is 4 times as far from Ridge as it is from Harbor. What fraction of the distance from Harbor to Summit is the distance from Maple to Summit?
A. \(\frac{3}{20}\)
B. \(\frac{1}{4}\)
C. \(\frac{2}{5}\)
D. \(\frac{17}{20}\)
E. \(\frac{20}{17}\)
The stops are in this order:
\(H --- M ------------ R ----- S\)
\(H\) = Harbor, \(M\) = Maple, \(R\) = Ridge, \(S\) = Summit
Since Ridge is 3 times as far from Harbor as it is from Summit:
\(HR : RS = 3:1\)
So \(HR = \frac{3}{4}\) of \(HS\).
Since Maple is 4 times as far from Ridge as it is from Harbor:
\(MR : HM = 4:1\)
So \(HM = \frac{1}{5}\) of \(HR\).
Choose \(HS = 20\), since 20 is the least common multiple of 4 and 5.
Then:
\(HR = \frac{3}{4} * 20 = 15\)
\(RS = 5\)
And:
\(HM = \frac{1}{5} * 15 = 3\)
\(MR = 12\)
So the diagram is:
\(H -(3)-- M ------(12)------ R --(5)--- S\)
The distance from Maple to Summit is:
\(MS = MR + RS = 12 + 5 = 17\)
The full distance from Harbor to Summit is:
\(HS = 20\)
Therefore, the required fraction is:
\(\frac{17}{20}\)
Answer: D
