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Bunuel
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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne 20 Apr 2020, 09:40
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95% (hard)

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30% (03:13) correct 70% (03:51) wrong based on 94 sessions

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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. 31.2 m
B. 31.8 m
C. 32.8 m
D. 43.4 m
E. 56.6 m

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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne 20 Apr 2020, 10:04
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Bunuel
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. 30.8 m
B. 31.8 m
C. 32.8 m
D. 43.4 m
E. 56.6 m

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P travels a distance of 4*8+5*8+6*8+......=400............8(4+5+6..+n)=400......4+5+6+...n=50
We can count and see what is n, as 50 is a small number or we could have used the formula of 'sum of first n integer-sum of first 3 integer=400'.

So 4+5+6+7+8+9+10+1 = 50......,
Thus, it covers 8(4+5+6+..10)=392 in 8*7 or 56 secs, and remaining 8 m @11m/s in 8/11 or 0.73 secs..
Total 56.73 secs..

In 56.73 secs, Q will travel 56.73*65=368.8m, so P can give a head start of 400-368.8 or 31.2 to Q
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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne 21 Apr 2020, 10:29
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Bunuel
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. 30.8 m
B. 31.8 m
C. 32.8 m
D. 43.4 m
E. 56.6 m

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Hello Bunuel, Please help with the solution. I am getting 31.2 m
Thanks in advance.
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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne 05 Nov 2020, 05:35
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chetan2u
Bunuel
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. 30.8 m
B. 31.8 m
C. 32.8 m
D. 43.4 m
E. 56.6 m

Are You Up For the Challenge: 700 Level Questions

P travels a distance of 4*8+5*8+6*8+......=400............8(4+5+6..+n)=400......4+5+6+...n=50
We can count and see what is n, as 50 is a small number or we could have used the formula of 'sum of first n integer-sum of first 3 integer=400'.

So 4+5+6+7+8+9+10+1 = 50......,
Thus, it covers 8(4+5+6+..10)=392 in 8*7 or 56 secs, and remaining 8 m @11m/s in 8/11 or 0.73 secs..
Total 56.73 secs..

In 56.73 secs, Q will travel 56.73*65=368.8m, so P can give a head start of 400-368.8 or 31.2 to Q
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why in 56.73 secs, will Q travel 56.73*65=368.8m?
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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne 03 May 2022, 10:12
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chetan2u
Bunuel
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. 30.8 m
B. 31.8 m
C. 32.8 m
D. 43.4 m
E. 56.6 m

Are You Up For the Challenge: 700 Level Questions

P travels a distance of 4*8+5*8+6*8+......=400............8(4+5+6..+n)=400......4+5+6+...n=50
We can count and see what is n, as 50 is a small number or we could have used the formula of 'sum of first n integer-sum of first 3 integer=400'.

So 4+5+6+7+8+9+10+1 = 50......,
Thus, it covers 8(4+5+6+..10)=392 in 8*7 or 56 secs, and remaining 8 m @11m/s in 8/11 or 0.73 secs..
Total 56.73 secs..

In 56.73 secs, Q will travel 56.73*65=368.8m, so P can give a head start of 400-368.8 or 31.2 to Q

why in 56.73 secs, will Q travel 56.73*65=368.8m?
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Q travels at a steady rate of 6.5 m every second so in 56.73 seconds, it will travel 6.5 * 56.73 meters = 368.8 meters
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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne 03 May 2022, 11:27
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Given: 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.

Asked: 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?

4*8 + 5*8 + 6*8 + 7*8 + 8*8 + 9*8 + 10*8 = 392
Time taken by P to cover 400 m distance = 8*7 + 8/11 = 56 8 /11 seconds
Distance covered by Q in 56 8/11 seconds = 6.5 * 56 + 6.5 * 8/11 = 364 + 4.72 = 368.73 meters

P can give Q a lead of = 400 - 368.72 meters = 31.27 meters

IMO A
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P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the ne 29 Dec 2025, 23:49
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