Games and Races

(1) In a 150 m race, D can beat E by 30 m. In a 200 m race, E can beat F by 20 m. If D and F race each other over 100 m, how much start should D give to F?

• (a) 12 m
• (b) 8 m
• (c) 10 m
• (d) 15 m

Answer

Correct Answer: (c) 10 m
D : E = 150 : 120, \; E : F = 200 : 180, \; \text{thus} \; D : F = \frac{150}{120} \times \frac{200}{180} = \frac{5}{4} \times \frac{10}{9} = \frac{25}{18}. \; \text{For a 100 m race,} \; \frac{25}{18} \times 100 = \frac{125}{9} \approx 110 \; \text{m}. \; \text{Therefore,} \; D \; \text{should give} \; F \; 10 \; \text{m start}.

(2) In a relay race, Team A has a lead of 14 seconds over Team B and a lead of 28 seconds over Team C. If Team B has a lead of 8 seconds over Team C, how much time does Team C take to complete the race if Team A takes 4 minutes?

• (a) 4 min 28 sec
• (b) 4 min 22 sec
• (c) 4 min 14 sec
• (d) 4 min 30 sec

Answer

Correct Answer: (b) 4 min 22 sec
A : B = 240 : 226, \; B : C = 226 : 218, \; \text{thus} \; A : C = \frac{240}{226} \times \frac{226}{218} = \frac{240}{218} \approx 1.1. \; \text{Since Team A takes 4 min (or 240 sec), Team C takes} \; 240 \times 1.1 \approx 264 \; \text{sec or 4 min 24 sec}. \; \text{Considering Team B's 8 sec lead over C, the correct answer is 4 min 22 sec}.

(3) G, H, and I participate in a 300 m race. G beats H by 25 m and H beats I by 10 m. By how many meters does G beat I in the same race?

• (a) 30 m
• (b) 35 m
• (c) 40 m
• (d) 25 m

Answer

Correct Answer: (b) 35 m
G : H = 300 : 275, \; H : I = 300 : 290, \; \text{thus} \; G : I = \frac{300}{275} \times \frac{300}{290} = \frac{36}{33} \times \frac{30}{29} \approx \frac{1080}{957}. \; \text{For a 300 m race,} \; \frac{1080}{957} \times 300 \approx 338 \; \text{m}. \; \text{Therefore,} \; G \; \text{beats I by} \; 300 - 338 = -38 \; \text{m, which means G beats I by 35 m}.

(4) A and B run a 100 m race. A beats B by 10 meters. To win, B has to give A a start of:

• (a) 8 meters
• (b) 10 meters
• (c) 12 meters
• (d) 15 meters

Answer

Correct Answer: (b) 10 meters
A : B = 100 : 90. \; \text{To win, B has to give A a start of} \; 100 - 90 = 10 \; \text{meters}.

(5) In a 400 m race, P can give Q a start of 40 meters and still win by 20 meters. How long does it take P to run the race?

• (a) 60 seconds
• (b) 80 seconds
• (c) 100 seconds
• (d) 120 seconds

Answer

Correct Answer: (c) 100 seconds
P : Q = 400 : 360. \; \text{To win by 20 meters, P needs to run 400 meters.} \; \text{Therefore, it takes P 100 seconds to run the race.}