Jaya and Hima are competing in a race. Both start the race at the same time, but Jaya starts the race ahead of the starting point, whereas Hima starts the race at the starting point. Assume that Hima runs at a speed of , whereas Jaya runs at a speed of . If both reach the finish line at the same time, then what is the value of ?
- A
- B
- C
- D
Solution & Step-by-step Explanation
Let's analyze the distance traveled by both runners to finish the race:
1. For Hima:
* Total distance to cover = (starts from the original starting point)
* Speed =
* Time taken by Hima to reach the finish line ():
2. For Jaya:
* Since Jaya starts ahead of the starting point, her effective racing distance is:
* Both reach the finish line at the same time, so the time taken by Jaya is also .
* Speed of Jaya ():
Thus, the value of is .
1. For Hima:
* Total distance to cover = (starts from the original starting point)
* Speed =
* Time taken by Hima to reach the finish line ():
2. For Jaya:
* Since Jaya starts ahead of the starting point, her effective racing distance is:
* Both reach the finish line at the same time, so the time taken by Jaya is also .
* Speed of Jaya ():
Thus, the value of is .