Question : Savitha and Parnika decided to run a 2250 m long race on a track as long as the length of the race. But Savitha gave Parnika a 396 m head start and also allowed her to start 9 seconds before Savitha started running. Parnika ran at 6 m per second and Savitha caught up with Parnika 250 seconds after Savitha started running. What was Savitha's speed (in m/s) during the race?
Option 1: 7.2
Option 2: 7.8
Option 3: 8
Option 4: 7.5
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Correct Answer: 7.5
Solution : Let us denote Savitha's speed as $s$ m/s. Since Parnika started 9 seconds before Savitha, the time Parnika ran is $(t+9)$ seconds. The distance Parnika ran = $6×(t+9)$ metres. Savitha started 250 seconds after Parnika and caught up with her. ⇒ The distance Savitha ran = $s\times t$ metres Parnika had a head start of 396 metres. According to the question, $6×(t+9)+396=s×t$ ⇒ $6×(t+9)+396=2250$ ⇒ $6t+54+396=2250$ ⇒ $6t=1800$ $\therefore t=300$ seconds Now, Speed $=\frac{\text{Distance}}{\text{Time}}=\frac{2250}{300}= 7.5$ m/s Hence, the correct answer is 7.5.
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