(a) Total metabolic rate as a function of walking and running speed, normalized by body mass, showing common tangent constructions for optimal walk–rest and walk–run mixtures. (b) Walk–run–rest fractions shown. As the average speed increases, the energy optimal strategy changes from a mixture of resting and walking to pure walking to a walk–run mixture to pure running. (c) Energy per unit distance for walking, running, walk–run mixtures and walk–rest mixtures. The mixture strategies (dotted lines) reduce the average energy per unit distance in the respective speed regimes, as shown. Note, the cost per distance of the mixtures is not a linear function of average speed, which is why the ‘common tangent construction’ is performed on the cost per time curves.