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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the next 8 seconds, 6 m/s for the next 8 and so on. Q cycles at a constant speed of 6.5 m/s throughout. If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q? 
  • a)
    43.4 m 
  • b)
    56.6 m 
  • c)
    32.1 m 
  • d)
    P cannot give a lead as Q is always ahead of P
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne...

Calculation of Lead Distance

To calculate the lead distance that P can give Q and still finish at the same time, we need to first determine the time taken by both P and Q to complete the race.

Time taken by P to complete the race:
- P cycles at varying speeds for 8 seconds each.
- Total time taken by P = 8 + 8 + 8 + ... (until the total distance of 400m is covered)
- Total time taken by P = 8 * (1/4 + 1/5 + 1/6 + ...)
- Total time taken by P can be calculated as 8 * (1/4 + 1/5 + 1/6 + ...) = 8 * 1.466 = 11.728 seconds

Time taken by Q to complete the race:
- Q cycles at a constant speed of 6.5 m/s.
- Time taken by Q to cover 400m = 400 / 6.5 = 61.54 seconds

Lead Distance:
- Lead distance that P can give Q = Speed of Q * Time taken by P - 400m
- Lead distance = 6.5 * 11.728 - 400 = 32.1 meters

Therefore, option (c) 32.1m is the correct answer.
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Community Answer
P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne...
Distance covered by P in 8 sec = 4 * 8 = 32 m Distance covered by P in 16 sec = 32 + 5 * 8 = 72 m
Distance covered by P in 24 sec = 72 + 6 * 8 = 120 m
Distance covered by P in 32 sec = 120 + 7 * 8 = 176 m
Distance covered by P in 40 sec = 176 + 8 * 8 = 240 m
Distance covered by P in 48 sec = 240 + 9 * 8 = 312 m
Total distance in 48 sec = 312m
To cover balance 86 m with speed = 10 m/sec, time taken = 86/10 = 8.6 sec
So,
P would finish 400 m in 48 + 8.6 = 56.6 seconds. In 56.6 seconds,
Q cycles 56.6 * 6.5 = 367.9 m or B should have a 32.1 m
lead to result in a dead heat. The question is "If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?"
Hence, the answer is 32.1 m
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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the next 8 seconds, 6 m/s for the next 8 and so on. Q cycles at a constant speed of 6.5 m/s throughout. If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?a)43.4 mb)56.6 mc)32.1 md)P cannot give a lead as Q is always ahead of PCorrect answer is option 'C'. Can you explain this answer?
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