We correlate the strength of the solvent-mediated attraction of a pair of hydrophobic solute molecules with the free energy of hydration of a single such molecule. This is done in the framework of a particular model but the results may be more general. When the model parameters are chosen to represent methane as the solute in water it is found that over the relevant temperature range the strength of the attraction, expressed as a multiple of the thermal energy kT, increases nearly linearly with increasing hydration free energy expressed in the same units. In the middle of the temperature range studied the strength of the attraction is roughly one-third of the hydration free energy.