It takes Evan 6 3/4 to mow 3 lawns. It takes 2 1/3 hours to mow me. Gals lawn and 1 3/4 hot mow Ms. Lee’s lawn. How many hours does it take Evan to mow the third lawn?

[tex]t=6\frac{3}{4}-2\frac{1}{3}-1\frac{3}{4}\\ t=\frac{6(4)+3}{4}-\frac{2(3)+1}{3}-\frac{1(4)+3}{4}\\ t=\frac{24+3}{4}-\frac{6+1}{3}-\frac{4+7}{4}\\ t=\frac{27}{4}-\frac{7}{3}-\frac{7}{4}\\ t=\frac{27}{4}-\frac{7}{4}-\frac{7}{3}\\ t=\frac{27-7}{4}-\frac{7}{3}\\ t=\frac{20}{4}-\frac{7}{3}\\ t=5-\frac{7}{3}\\ t=5.\frac{3}{3}-\frac{7}{3}\\ t=\frac{5(3)}{3}-\frac{7}{3}\\ t=\frac{15}{3}-\frac{7}{3}\\ t=\frac{15-7}{3}\\ t=\frac{8}{3}\\ t=\frac{6+2}{3}\\ t=\frac{6}{3}+\frac{2}{3}[/tex]

[tex]t=2+\frac{2}{3}\\ t=2\frac{2}{3}[/tex]

thaovtp1407 thaovtp1407 · Answer 2 · 2020-04-27T03:51:45+02:00

Answer:

It takes Evan [tex]2\frac{2}{3}\ hours[/tex] to mow the third lawn

Step-by-step explanation:

Given that:

It takes Evan 6 3/4 to mow 3 lawns

<=> [tex]6\frac{3}{4}=\frac{27}{4}\ \text{hours}[/tex]

It takes 2 1/3 hours to mow Mr. Gals lawn (first lawn)

<=> [tex]2\frac{1}{3}=\frac{7}{3}\ \text{hours}[/tex]

It takes 1 3/4 hot mow Ms. Lee’s lawn (second lawn)

<=> [tex]1\frac{3}{4}=\frac{7}{4}\ \text{hours}[/tex]

Now,Time taken by Evan to mow the third lawn

[tex]=\frac{27}{4}-\frac{7}{3}-\frac{7}{4}[/tex]

= [tex]\frac{81-28-21}{12}[/tex]

= [tex]\frac{32}{12} = \frac{8}{3}[/tex]

= [tex]2\frac{2}{3}\ hours[/tex]

It takes Evan [tex]2\frac{2}{3}\ hours[/tex] to mow the third lawn