09 - Number of Leaps to Take to Catch the Lead

Let
c = number of leaps of cat
d = number of leaps of dog
 

$\dfrac{c}{d} = \dfrac{4}{3}$

$c = \dfrac{4d}{3}$
 

2 leaps of dog = 3 leaps of cat = L
$\text{1 leap of dog} = \dfrac{L}{2}$

$\text{1 leap of cat} = \dfrac{L}{3}$
 

For the dog to catch the cat:
$(c + 50)\left( \dfrac{L}{3} \right) = d \left( \dfrac{L}{2} \right)$

$\left(\dfrac{4d}{3} + 50 \right)\left( \dfrac{1}{3} \right) = d \left( \dfrac{1}{2} \right)$

$d = 300 ~ \text{leaps}$   ←   answer