Elly and Danny enjoy building radios, a task suited to a single individual. Danny builds radios at a rate of $2$ per hour, but when Elly is working on her own radio beside him, his rate accelerates to $3$ per hour.
Elly builds radios at a rate of $4$ per hour but accelerates to $5$ per hour when Danny is working alongside her. One afternoon, they are bored and decide to assemble $21$ radios they found in Elly’s attic.
How long will it take the two of them to finish all the radios?