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| Get The Distance (Posted on 2007-05-15) |
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If Gideon had driven for 20 minutes less than the time he would have driven if he had driven 20 kilometers less than he did drive but at two-thirds the speed at which he drove, he would have driven 10 kilometers less than he did.
However, if he had driven 20 minutes longer than the time he would have driven if he had driven 10 kilometers less than he did drive but at three-quarters the speed at which he drove, he would have driven 20 kilometers further.
How far did Gideon drive?
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Submitted by K Sengupta
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Rating: 5.0000 (1 votes)
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Solution:
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(Hide)
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Let us assume that Gideon covered x kilometers in y minutes, so that he traveled at a speed of x/y kilometers per minute.
Then, by the problem,
{3y(x-20)/2x – 20}(x/y) = x – 10….(i)
{4y(x-10)/3x + 20}(x/y) = x + 10….(ii)
From (i), we obtain:
y = 40x/(x- 40) …….(iii)
Also, from (ii), we obtain:
y = 60x/(100-x)
Thus, 40x/(x- 40) = 60x/(100-x), giving:
x = 64, so that:
y = 320/3
Consequently, Gideon drove for a distance of 64 kilometers driving for a duration of 320/3.
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Also refer to an alternate methodology posted by Charlie in this location
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Source: Adapted from a problem which appeared in Test Of Reasoning 4 by Philip J. Carter and Ken A. Russell
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Subject |
Author |
Date |
 | solution | Charlie | 2007-05-15 15:56:02 |
| solution | hoodat | 2007-05-15 13:47:32 |
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