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# Speed Question

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Retired Moderator
Joined: 18 Jul 2008
Posts: 921

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27 Apr 2009, 15:43
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A 400-meter runner spent 4 more seconds on the first half of the distance than he did on the second. If the runner finished the 400-meter distance in 50 seconds, what was his average speed for the first 200 meters?

a) 24 1/3 kmh
b) 25 1/3 kmh
c) 26 2/3 kmh
d) 27 2/3 kmh
e) 29 1/12 kmh

This is a pretty easy one, but I couldn't understand this:

Answer: Denote x the time the runner spent on the first 200 meters. Then, x + (x - 4) = 50 from where x = 27 seconds

Why can't I say X+4 = first 200 meters, X = last 200 meters

Then x+4 + x = 50?
Manager
Joined: 19 Aug 2006
Posts: 233

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27 Apr 2009, 18:00
A 400-meter runner spent 4 more seconds on the first half of the distance than he did on the second. If the runner finished the 400-meter distance in 50 seconds, what was his average speed for the first 200 meters?

a) 24 1/3 kmh
b) 25 1/3 kmh
c) 26 2/3 kmh
d) 27 2/3 kmh
e) 29 1/12 kmh

This is a pretty easy one, but I couldn't understand this:

Answer: Denote x the time the runner spent on the first 200 meters. Then, x + (x - 4) = 50 from where x = 27 seconds

Why can't I say X+4 = first 200 meters, X = last 200 meters

Then x+4 + x = 50?

There's no reason you cannot - and you will still get x=27sec for the 1st 200 meters.

x+4 - 1st 200 meters
x - the last 200 meters

x+x+4=50
2x=46
x=23

23+3=27sec

However, I seem to have a problem with calculating the final answer - is it B?
Retired Moderator
Joined: 18 Jul 2008
Posts: 921

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28 Apr 2009, 06:33
Thanks for the explanation.

Manager
Joined: 19 Aug 2006
Posts: 233

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28 Apr 2009, 17:39
Thanks for the explanation.

Would you care to show your calculations?
SVP
Joined: 29 Aug 2007
Posts: 2457

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28 Apr 2009, 19:26
A 400-meter runner spent 4 more seconds on the first half of the distance than he did on the second. If the runner finished the 400-meter distance in 50 seconds, what was his average speed for the first 200 meters?

a) 24 1/3 kmh
b) 25 1/3 kmh
c) 26 2/3 kmh
d) 27 2/3 kmh
e) 29 1/12 kmh

Its same. Either gives the same result.

1. x+x-4 = 50
x = 27
First half time = x = 27
Second half time = x - 4 = 27-4 = 23

Avg speed for the first half = 200m /x = 200m/27 = 200m/{27/(60*60)} per hour = (200m*60*60)/(27) = 200m*20*20/3 = 80km/3 = 26 2/3 per hour.

2. x+4+x = 50
x = 23
First half time = x +4 = 27
Second half time = x = 23

Avg speed for the first half = 200m /(x+4) = 200m/(23+4) = 200m/{27/(60*60)} per hour = (200m*60*60)/(27) = 200m*20*20/3 = 80km/3 = 26 2/3 per hour.
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Manager
Joined: 13 Jan 2009
Posts: 168

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29 Apr 2009, 03:50
GMAT TIGER wrote:
A 400-meter runner spent 4 more seconds on the first half of the distance than he did on the second. If the runner finished the 400-meter distance in 50 seconds, what was his average speed for the first 200 meters?

a) 24 1/3 kmh
b) 25 1/3 kmh
c) 26 2/3 kmh
d) 27 2/3 kmh
e) 29 1/12 kmh

Its same. Either gives the same result.

1. x+x-4 = 50
x = 27
First half time = x = 27
Second half time = x - 4 = 27-4 = 23

Avg speed for the first half = 200m /x = 200m/27 = 200m/{27/(60*60)} per hour = (200m*60*60)/(27) = 200m*20*20/3 = 80km/3 = 26 2/3 per hour.

2. x+4+x = 50
x = 23
First half time = x +4 = 27
Second half time = x = 23

Avg speed for the first half = 200m /(x+4) = 200m/(23+4) = 200m/{27/(60*60)} per hour = (200m*60*60)/(27) = 200m*20*20/3 = 80km/3 = 26 2/3 per hour.

Thanks GMAT TIGER! Good explanation.
Manager
Joined: 19 Aug 2006
Posts: 233

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29 Apr 2009, 06:55
GMAT TIGER wrote:
A 400-meter runner spent 4 more seconds on the first half of the distance than he did on the second. If the runner finished the 400-meter distance in 50 seconds, what was his average speed for the first 200 meters?

a) 24 1/3 kmh
b) 25 1/3 kmh
c) 26 2/3 kmh
d) 27 2/3 kmh
e) 29 1/12 kmh

Its same. Either gives the same result.

1. x+x-4 = 50
x = 27
First half time = x = 27
Second half time = x - 4 = 27-4 = 23

Avg speed for the first half = 200m /x = 200m/27 = 200m/{27/(60*60)} per hour = (200m*60*60)/(27) = 200m*20*20/3 = 80km/3 = 26 2/3 per hour.

2. x+4+x = 50
x = 23
First half time = x +4 = 27
Second half time = x = 23

Avg speed for the first half = 200m /(x+4) = 200m/(23+4) = 200m/{27/(60*60)} per hour = (200m*60*60)/(27) = 200m*20*20/3 = 80km/3 = 26 2/3 per hour.

Thanks, made an error in the final calculation. This clears it.
Re: Speed Question   [#permalink] 29 Apr 2009, 06:55
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