Shortcut Trick
Time taken by P to complete 500 m = 500 ÷ (2 × 5/18) = 900 seconds.
Since P beats Q by 60 s, time taken by Q = 900 + 60 = 960 seconds.
Q gets a 20 m head start, so distance run by Q = 500 − 20 = 480 m.
Speed of Q in m/s = 480 ÷ 960 = 0.5 m/s.
Speed of Q in kmph = 0.5 × (18/5) = 1.8 kmph.
∴ The correct answer is 1.8 kmph.
Alternate Method
Given:
⇒ Total race distance = 500 m
⇒ Speed of P = 2 kmph
⇒ Head start of Q = 20 m
⇒ P beats Q by = 60 seconds
Formula Used:
⇒ Time = Distance ÷ Speed
⇒ Speed in kmph = Speed in m/s × 18/5
Calculations:
⇒ Speed of P in m/s = 2 × (5/18) = 5/9 m/s
⇒ Time taken by P to complete 500 m = 500 ÷ (5/9) = (500 × 9) ÷ 5 = 900 seconds
⇒ Since P beats Q by 60 seconds, time taken by Q to reach the finish line = 900 + 60 = 960 seconds
⇒ Q received a head start of 20 m, so Q covers only 500 − 20 = 480 m
⇒ Speed of Q in m/s = Distance ÷ Time = 480 ÷ 960 = 0.5 m/s
⇒ Converting Q's speed to kmph = 0.5 × (18/5) = 1.8 kmph
∴ The correct answer is 1.8 kmph.
Additional Information
Head Start in a Race
If A gives B a head start of x meters in a race of length L, then A must cover L meters, but B only needs to cover (L − x) meters.
Beating by Time
If A beats B by t seconds, it means B arrives t seconds later than A at the finish line. Thus, Time of B = Time of A + t.
Unit Conversion for Speed
To convert kmph to m/s, multiply the value by 5/18. To convert m/s to kmph, multiply by 18/5.