Question : A runner starts running from a point at 5:00 am at the speed of 10 km/hr. The second runner starts from the same point at 8:00 am in the same direction with a speed of 15 km/hr. At what time of the day will the second runner will overtake the first runner?
Option 1: 2:00 pm
Option 2: 12:30 pm
Option 3: 12:00 pm
Option 4: 1:00 pm
Correct Answer: 2:00 pm
Solution :
Let's denote the time (in hours) the second runner runs as t hours.
The distance covered by the first runner in time (t + 3) hrs = 10 × (t + 3) km.
The distance covered by the second runner in time t hrs = 15t km.
According to the question at the time of overtaking
⇒ 10 × (t + 3) = 15×t
⇒ 10t + 30 =15t
⇒ 5t = 30
⇒ t = $\frac{30}{5}$
⇒ t = 6 hours
So, the second runner will overtake the first at 2:00 pm.
Hence, the correct answer is 2:00 pm
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