A car has an engine that develops constant torque of 150 Nm at speeds from 0 to 1800
rpm. At higher speeds, the torque decreases linearly from 150 Nm at 1800 rpm to 0 Nm
at 2800 rpm. The maximum speed of the engine is 2800 rpm. The car’s roadwheels are
585 mm in diameter. You are one of a team whose task is to design a gearbox which
provides gear ratios (ratio of engine speed to roadwheel speed) of 2.05 and 1.62. All
gears in the gearbox should have the same circular pitch. Between the gearbox and the
roadwheels there is a differential gear with a gear ratio of exactly 1.

Question

A car has an engine that develops constant torque of 150 Nm at speeds from 0 to 1800 
rpm. At higher speeds, the torque decreases linearly from 150 Nm at 1800 rpm to 0 Nm 
at 2800 rpm. The maximum speed of the engine is 2800 rpm. The car’s roadwheels are 
585 mm in diameter. You are one of a team whose task is to design a gearbox which 
provides gear ratios (ratio of engine speed to roadwheel speed) of 2.05 and 1.62. All 
gears in the gearbox should have the same circular pitch. Between the gearbox and the 
roadwheels there is a differential gear with a gear ratio of exactly 1.