Difference between revisions of "2007 Cyprus MO/Lyceum/Problem 3"
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==Problem== | ==Problem== | ||
− | A cyclist drives form town A to town B with velocity <math>40 \frac{\mathrm{km}}{\mathrm{h}}</math> and comes back with velocity <math>60 \frac{\mathrm{km}}{\mathrm{h}}</math>. The mean velocity in <math>\frac{\mathrm{km}}{\mathrm{h}}</math> for the total distance is | + | A cyclist drives form town A to town B with velocity <math>40 \frac{\mathrm{km}}{\mathrm{h}}</math> and comes back with velocity <math>60 \frac{\mathrm{km}}{\mathrm{h}}</math>. The [[mean]] velocity in <math>\frac{\mathrm{km}}{\mathrm{h}}</math> for the total distance is |
<math> \mathrm{(A) \ } 45\qquad \mathrm{(B) \ } 48\qquad \mathrm{(C) \ } 50\qquad \mathrm{(D) \ } 55\qquad \mathrm{(E) \ } 100</math> | <math> \mathrm{(A) \ } 45\qquad \mathrm{(B) \ } 48\qquad \mathrm{(C) \ } 50\qquad \mathrm{(D) \ } 55\qquad \mathrm{(E) \ } 100</math> | ||
==Solution== | ==Solution== | ||
− | Let the distance from town A to town B, in kilometers, be <math>d</math>. | + | Let the [[distance]] from town A to town B, in kilometers, be <math>d</math>. |
The time it took the cyclist to travel from <math>A</math> to <math>B</math> was <math>\frac{d}{40}</math> hours. | The time it took the cyclist to travel from <math>A</math> to <math>B</math> was <math>\frac{d}{40}</math> hours. | ||
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==See also== | ==See also== | ||
− | + | {{CYMO box|year=2007|l=Lyceum|num-b=2|num-a=4}} | |
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Revision as of 15:17, 6 May 2007
Problem
A cyclist drives form town A to town B with velocity and comes back with velocity . The mean velocity in for the total distance is
Solution
Let the distance from town A to town B, in kilometers, be .
The time it took the cyclist to travel from to was hours.
The time it took the cyclist to travel from to was hours.
The cyclist's mean velocity was
See also
2007 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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