P, Q and R are in a cycle race of 4500 meters. P cycles twice as fast as Q. R cycles 1/3 as fast as Q. R completes the race in 45 minutes. Then where was Q from the finishing line when P finished the race?

Question: P, Q and R are in a cycle race of 4500 meters. P cycles twice as fast as Q. R cycles 1/3 as fast as Q. R completes the race in 45 minutes. Then where was Q from the finishing line when P finished the race?

Solution:
Given that,
Race = 4500 m
R finishes in 45 min
∴ speed of R = 4500/45 = 100 m/min

R’s speed = (1/3) Q’s speed
∴ Q’s speed = 300 m/min

And, P’s speed = 2 × Q’s speed = 600 m/min

∴ Time for P to finish 4500 m = 4500/600 = 7.5 min
In 7.5 min, Q covers = 300 × 7.5 = 2250 m

∴ Distance left for Q = 4500 - 2250 = 2250 m

So Q was 2250 meters from the finishing line when P finished.