MATHCOUNTS® Problem of the Week Archive
A Ride in the Park – March 18, 2013
Problems & Solutions
The map shows several roads in and around Sasha’s local
park. On Monday, Sasha wanted to visit the sculpture garden
and see the fountain. So, that day Sasha rode her bike from
the park entrance down Garden Lane, then left onto Fountain
Way, and finally to the park exit. On Wednesday Sasha
wanted to see the fountain again. So, Wednesday Sasha
took Lark’s Pass, and made a left onto Fountain Way to
the park exit. On Friday, Sasha opted not to visit the
sculpture garden or the fountain, so she just took Park
Road from the park entrance directly to the park exit.
How many more meters did Sasha ride on Monday than she rode on Friday to get from the park
entrance to the park exit? Express your answer as a decimal to the nearest tenth.
To determine the distance she rode her bike on Fountain Way, we can use the Pythagorean Theorem. We
have 64.52 + b2 = 167.72 → 4160.25 + b2 = 28,123.29 → b2 = 23,963.04 → = b = 154.8 m. Thus, on Monday,
Sasha rode her bike a total of 64.5 + 154.8 = 219.3 m from the park entrance to the park exit. Sasha rode her
bike 167.7 m from the park entrance to the park exit. The difference is 219.3 – 167.7 = 51.6 m.
On Fountain Way, the distance from the fountain to the park exit is 7/9 the distance from the sculpture
garden to the park exit. What is the distance from the sculpture garden to the fountain via Fountain
Way? Express your answer as a decimal to the nearest tenth.
We are told that the distance from the fountain to the park exit is 7/9 the distance from the sculpture
garden to the park exit. It then follows that the distance from the sculpture garden to the fountain is 2/9 the
distance from the sculpture garden to the park exit which, in the previous problem, was determined to be
154.8 m. Therefore, on Fountain Way, the distance from the sculpture garden to the fountain is 2/9 × 154.8 =
34.4 m.
What is the total distance that Sasha rode her bike from the park entrance to the park exit on Monday,
Wednesday and Friday? Express your answer as a decimal to the nearest tenth.
From the previous problem we know that Sasha rode her bike 219.3 m from the park entrance to the park
exit. We can use the Pythagorean Theorem to determine the distance Sasha rode her bike on Lark’s Pass.
Based on the previous problem, we have 64.52 + 34.42 = c2 → 4160.25 + 1183.36 = c2 → 5343.61= c2 →
c = 73.1 m. The distance Sasha rode her bike on Fountain Way from the fountain to the park exit was
154.8 − 34.4 = 120.4 m. So, on Wednesday, Sasha rode her bike 73.1 + 120.4 = 193.5 m from the park
entrance to the park exit. On Friday, Sasha rode her bike 167.7 m from the park entrance to the park exit.
Therefore, the total distance that Sasha rode her bike on Monday, Wednesday and Friday was
219.3 + 193.5 + 167.7 = 580.5 m.