Answer:
Option B
Step-by-step explanation:
Time taken by Nathan to completethe task = 4 hours
[tex]\text{Work done by Nathan in 1 hour = $\dfrac{x}{4}$}[/tex]
Time taken by Elijah to complete the task = 3 hours
[tex]\sf \text{Work done by Elijah in 1 hour=$\dfrac{x}{3}$}[/tex]
They work together to complete the work
[tex]\text{Work done by both in 1 hour = $ \dfrac{x}{4}+\dfrac{x}{3}$}[/tex]
[tex]\sf =\dfrac{x*3}{4*3}+\dfrac{x*4}{3*4}\\\\=\dfrac{3x}{12}+\dfrac{4x}{12}\\\\=\dfrac{7x}{12}[/tex]
[tex]\text{Time taken by both= x $\div$ $\dfrac{7x}{12}$}[/tex]
[tex]\sf = x * \dfrac{12}{7x}\\\\ = \dfrac{12}{7}[/tex]
≈ 1.7 hours
