Problem $13\mathrm{.}024-$ Compound reverted gear train

A gearbox is to be designed with a compound reverted gear train that transmits $25$ horsepower with an input speed of $\backslash (1500\backslash$mathrm$\{$rev$\}/\backslash$mathrm$\{$min$\}\backslash ).$ The output should deliver the power at a rotational speed in the range of $280$ to $\backslash (300\backslash$mathrm$\{$rev$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Spur gears with $\backslash (20^\{\backslash$circ$\}\backslash )$ pressure angle are to be used. Determine suitable numbers of teeth for each gear, to minimize the gearbox size while providing an output speed within the specified range. Be sure to avoid an interference problem in the teeth.

The suitable numbers of teeth for each gear to minimize the gearbox size while providing an output speed within the specified range are

The number of teeth in gear $2$ is

The number of teeth in gear $3$ is

The number of teeth in gear $4$ is

The number of teeth in gear $5$ is

$\backslash (\backslash$checkmark $\backslash )$ teeth

$*$ teeth

$\backslash (\backslash$checkmark $\backslash )$ teeth

$*$ teeth