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*