JM / JK =JN/JL
JM / 36 = 60/48
JM = 36 * 60 / 48 = 45 units (obviously not drawn to scale ) MK = JM - 36 = 9
We know that $\triangle JKL \sim \triangle JMN$ by $AA$ similarity ($\angle JKL \cong \angle JMN$ and $\angle JLK \cong \angle JNM$ because $KL \parallel MN$). Therefore,
$$\frac{JK}{JM} = \frac{JL}{JN},$$
$$\frac{36}{JM} = \frac{48}{60}, $$
$$JM = 45. $$
Given that $JM=45$, we see that $MK = JM - JK$, and $JK=36$ using the similarity ratio above. Thus, $MK = 45 - 36 = \boxed{9}.$