Problema Solution

Working together, Tanner and Joel can grade their students' projects in 2 hours. Working alone, it would take Tanner 2 hours longer than it would take Joel to grade the projects. How long, working alone, would it take Joel to grade the projects?

Answer provided by our tutors

let


t = the hours Tanner needs to to grade the projects alone


1/t projects per hour is the rate of Tanner


j = the hours Joel needs to to grade the projects alone


1/j projects per hour is the rate of Joel


Working alone, it would take Tanner 2 hours longer than it would take Joel to grade the projects:


t = 2 + j


Tanner and Joel can grade their students' projects in 2 hours thus their together rate is: 1/2 projects per hour


1/t + 1/j = 1/2


plug t = 2 + j into the last equation:


1/(2 + j) + 1/j = 1/2


by solving we find:


j = 3.24 hr approximately


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it would take 3.24 hr approximately for Joel to grade the projects alone.