help similar triangles

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, $MK = 45 - 36 = \boxed{9}.$