  We estimate a characteristic timescale for star formation in the spiral arms
of disk galaxies, going from atomic hydrogen (HI) to dust-enshrouded massive
stars. Drawing on high-resolution HI data from The HI Nearby Galaxy Survey and
24$\mu$m images from the Spitzer Infrared Nearby Galaxies Survey we measure the
average angular offset between the HI and 24$\mu$m emissivity peaks as a
function of radius, for a sample of 14 nearby disk galaxies. We model these
offsets assuming an instantaneous kinematic pattern speed, $\Omega_p$, and a
timescale, t(HI-->24$\mu$m), for the characteristic time span between the dense
\hi phase and the formation of massive stars that heat the surrounding dust.
Fitting for $\Omega_p$ and t(HI-->24$\mu$m), we find that the radial dependence
of the observed angular offset (of the \hi and 24$\mu$m emission) is consistent
with this simple prescription; the resulting corotation radii of the spiral
patterns are typically $R_{cor}\simeq 2.7 R_{s}$, consistent with independent
estimates. The resulting values of t(HI-->24$\mu$m) for the sample are in the
range 1--4 Myr. We have explored the possible impact of non-circular gas
motions on the estimate of t(HI-->24$\mu$m) and have found it to be
substantially less than a factor of 2. This implies that a short timescale for
the most intense phase of the ensuing star formation in spiral arms, and
implies a considerable fraction of molecular clouds exist only for a few Myr
before forming stars. However, our analysis does not preclude that some
molecular clouds persist considerably longer. If much of the star formation in
spiral arms occurs within this short interval t(HI-->24$\mu$m), then star
formation must be inefficient, in order to avoid the short-term depletion of
the gas reservoir.
