emobaby987
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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, how long did it take yumi

A) 1 hour 20 minutes

B) 3 hours 20 minutes

C) 4 hours

D) 6 hours

Respuesta :

binabahtisrealp0wrkv
The answer is D because if the answer was 1 hour 20 minutes then that means that she took 2 hours And 20 minutes but she only took two hours longer than juan and juan took less time.   
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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.

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