Pulse-echo image generation requires knowing the time of flight (TOF) for ultrasound in tissue. TOF depends on propagation distance and the speed of sound (SOS). Conventional imaging systems assume SOS in tissue is constant with a value close to that for water. Adaptively focusing under varying assumptions about SOS can improve pulse-echo images and elicit local values for SOS. Regions (64x64 mm) with varying SOS were simulated. Contrast of images of a point-like scatterer at 50 mm, formed using a 32-element, linear array of 1.1 x 13 mm transducers, with center frequencies of 3.5 MHz, improved by 8-10 dB when actual SOS was taken into account. To implement an adaptive, synthetic-focus scheme, the variation of SOS and TOF in tissue must be modeled. We previously approximated TOF with integer-degree polynomials in range and azimuth to reduce image generation time for constant-SOS regions. Here the utility of these polynomials to describe regions with varying SOS was explored. Paths in an assumed SOS map with tissue-like variation, were matched to within 1.1% with a fourth-degree polynomial. If the coefficients of these polynomials can be estimated from measured backscattered signals via adaptive-focus imaging, then a polynomial description of SOS and TOF may lead to improved image quality along with SOS characterization in tissue.