Difficult# Bicycle Wheels

SATMAT-MSOXY4

An adult bike wheel with a $26$-inch diameter rotates through a turn of $ \frac { 8\pi }{ 13 } $ radians. A child's bike wheel with a $ 16 $ -inch diameter rotates through a turn of $ \frac { 3\pi }{ 4 } $ radians.

How much further does the adult bike travel than the child's bike? (No Calculator)