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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?


$162$ minutes


$170$ minutes


$172$ minutes


$174$ minutes


$180$ minutes

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