Question : In a 5 km race, S gave a 500 m head start to T. If they finished the race at the same time and the speed of T is 13.5 km/hr, the speed of S is:
Option 1: 15 km/hr
Option 2: 20 km/hr
Option 3: 17.5 km/hr
Option 4: 16.5 km/hr
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Correct Answer: 15 km/hr
Solution : Let the speed of S as \(v\) km/hr. Given that S gave a 500 m (or 0.5 km) head start to T, S has to run 5 km while T runs 4.5 km. Since they finish the race at the same time, their times are equal. $⇒\frac{\text{Distance of S}}{\text{Speed of S}} = \frac{\text{Distance of T}}{\text{Speed of T}}$ Substituting the given values into the equation, $⇒\frac{5}{v} = \frac{4.5}{13.5}$ $⇒v = \frac{5 \times 13.5}{4.5} = 15 $ Hence, the correct answer is 15 km/hr.
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