PSLE
At a walkathon, each participant completed either a 1-km route, a 2-km route or a 5-km route. ¹₂ of the participants completed the 1-km route, ⁵₁₂ of the participants completed the 2-km route and the rest completed the 5-km route. For every 1 km a participant walked, $6 was donated to charity. A total of $1890 was donated to charity.

1. What is the ratio of the number of participants who completed the 1-km route to the number who completed the 2-km route to the number who completed the 5-km route?
2. What is the total number of participants at the walkathon?

(a)
Fraction of the participants who completed 5-km route
= 1 - ¹₂ - ⁵₁₂
= 1 - ⁶₁₂ - ⁵₁₂
= 1 - ¹¹₁₂
= ¹₁₂

Ratio of participants who completed the different routes
1 km : 2 km : 5 km
6 : 5 : 1

(b)
For every 1 km a participant walked, $6 was donated to charity.

Total distance covered by the participants
= 1890 ÷ 6
= 315 km

	1-km	2-km	5-km	Total
Number	6 u	5 u	1 u	12 u
Value	1	2	5
Total value	6 u	10 u	5 u

Total distance that the participants covered
= 1 x 6 u + 2 x 5 u + 5 x 1 u
= 6 u + 10 u + 5 u
= 21 u

21 u = 315

1 u = 315 ÷ 21 = 15

Total number of participants
= 6 u + 5 u + 1 u
= 12 u
= 12 x 15
= 180

Answer(s): (a) 6 : 5 : 1; (b) 180