Problem of the Week
Problem C and Solution
Keep On Hopping
Problem
Joy Junior High School is running a unique fundraiser called “Hopping for Heart”.
Participants obtain pledges and complete a 5 km (5000 m) course as follows: run 70 metres;
then hop 15 metres; and then walk 35 metres. This cycle of running, hopping and walking
repeats until the 5 km course is completed. Note, the event is completed when the 5 km mark
is reached and this may occur during the running, hopping or walking part of a cycle.
What percentage of the entire course does a participant spend on each of the activities?
Solution
One complete cycle of running, hopping and walking is 70 + 15 + 35 = 120 m long. The
number of cycles is 5000 m is
125
2
5000
=
= 41 .
120
3
3
2
There are 41 complete cycles and 3 of another cycle. The total distance covered in 41 cycles is
41 × 120 = 4920 m. There are 5000 − 4920 = 80 m remaining. The participants will now run
70 m leaving another 10 m to complete. Normally, the participants would hop 15 m but since
there are only 10 m left, the participants will end the event hopping the final 10 m.
In the 41 complete cycles each participant will run 41 × 70 = 2870 m, hop 41 × 15 = 615 m,
and walk 41 × 35 = 1435 m.
Since each participant runs an extra 70 m, the total distance run by each participant is
2870 + 70 = 2940 m. Since each participant hops an extra 10 m, the total distance hopped by
each participant is 615 + 10 = 625 m. The total distance walked by each participant remains
unchanged at 1435 m. The percentages can now be determined.
Percentage of the total distance that each participant runs
2940
× 100%
=
5000
= 58.8%
Percentage of the total distance that each participant hops
625
=
× 100%
5000
= 12.5%
Percentage of the total distance that each participant walks
1435
=
× 100%
5000
= 28.7%
To complete the course, participants run 58.7% of the distance, hop 12.5% of the distance and
walk 28.7% of the distance.