Answer:
Option D - 6 hours
Step-by-step explanation:
Given : Yumi and Juan pick up litter along the highway at the same rate. Yumi picks up littler for 3 miles and takes two hours longer than juan, who picks up litter for 2 miles. if it took juan x hours.
To find : How long did it take Yumi
?
Solution :
Let the Juan's time be x hours.
Yumi takes two hours longer than Juan,
Yumi's time be x+2 hours.
Yumi's distance = 3 miles
Juan's distance = 2 miles
We know,
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
Juan's speed is
[tex]S_J=\frac{2}{x}[/tex]
Yumi's speed is
[tex]S_Y=\frac{3}{x+2}[/tex]
The speed of both were same,
So [tex]\frac{2}{x}=\frac{3}{x+2}[/tex]
[tex]2\times(x+2)=3x[/tex]
[tex]2x+4=3x[/tex]
[tex]x=4[/tex]
Juan's time is 4 hours and
Yumi's time is 4 + 2 = 6 hours.
Therefore, Option D is correct.
