A geometry problem by Sumukh Bansal

Geometry Level 2

Eddie and Missy are swimming laps in parallel lanes of a swimming pool at different constant speeds. They start simultaneously at opposite ends of the pool. They first pass each other when Eddie has swum 21.9456m. Both turn back when they reach the opposite ends, and they next pass each other when Eddie is 12.192m from Missy’s starting point. What is the length of a lap(in meter)? m means "meter"

The answer is 53.6448.

1 solution

Tarsem Singh Khalsa
Dec 18, 2017

Consider the length of a lap in pool is $x$ .

Speed of Eddie is $E$ and that of Missy is $M$

Let time $t=t_1$ when Eddie and Missy passes each other first time (when Eddie has swum 21.9456 m). So we can write

$E*t_1 = 21.9456$

$M*t_1 = x-21.9456$

${\frac EM} = {\frac {21.9456}{x-21.9456}}$

Let time $t=t_2$ when Eddie and Messy passes each other second time (when Eddie is 12.192 m from Missy's starting point).

$E*t_2 = x+12.192$

$M*t_2 = 2x-12.192$

${\frac EM} = {\frac {x+12.192}{2x-12.192}}$

...equating both the equations, we get...

${\frac EM} = {\frac {21.9456}{x-21.9456}} = {\frac {x+12.192}{2x-12.192}}$

$21.9456*(2x-12.192) = (x-21.9456)*(x+12.192)$

Solving for $x$ , we get

$x = 0$ or $x = 53.6448$

Since the length of pool can not be $0$ , the length of pool will be $53.6448$ meters.

A geometry problem by Sumukh Bansal

The answer is 53.6448.

1 solution

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