In speed and distance questions drawing a diagram helps in visualizing the problem and easy formulation of the equation.

Given InfoWe are given that Nicky runs at a speed of 3 meters/second for 12 seconds before Cristina starts running at a speed of 5 meters/second. We are asked to find the time for which Nicky has run before Cristina catches up with him.

ApproachWe know that

Distance = Speed * Time. Since we know the speed at which Nicky runs and his head start time we can calculate his head start distance. We also know the speed at which Cristina runs. Once Cristina starts running, they both will run for the same time before Cristina catches up with Nicky.

Since we know the running speeds of both Nicky and Cristina, we can calculate their distance covered in terms of a common variable i.e. the time taken. As Nicky had a headstart, the extra distance covered by Cristina will be equal to the head start distance which Nicky had.

Working OutRefer the below diagram

Head start time given to Nicky = 12 seconds

Speed at which Nicky runs = 3 meters/second

Distance covered by Nicky = 12 * 3 = 36 meters

Let the time taken by Cristina to catch up with Nicky be t.

Speed at which Cristina runs = 5 meters/second

Distance covered by Cristina in time t = 5t

Distance covered by Nicky in time t = 3t

Since distance covered by Cristina in time t is 36 meters more than that covered by Nicky in time t, we can write

5t = 3t + 36 i.e. t = 18 seconds.

This is the time taken by Cristina to catch up with Nick. Since we are asked to find the time taken by Nicky, we will add the 12 seconds head start he had. So time for which Nicky ran before Cristina caught up with him = 18 + 12 = 30 seconds.

Hope this helps

Regards

Harsh

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