yumi and juan pick up litter along the highway at the same rate. yumi picks up litter for 3 miles and takes…

yumi and juan pick up litter along the highway at the same rate. yumi picks up litter for 3 miles and takes 2 hours longer than juan, who picks up litter for 2 miles. if juan spent x hours picking up litter, the following equation models the situation.\n\n$\frac{2}{x}=\frac{3}{x + 2}$\n\nhow long did yumi spend picking up litter?\n\n1 hour 20 minutes\n3 hours 20 minutes\n4 hours\n6 hours

yumi and juan pick up litter along the highway at the same rate. yumi picks up litter for 3 miles and takes 2 hours longer than juan, who picks up litter for 2 miles. if juan spent x hours picking up litter, the following equation models the situation.\n\n$\frac{2}{x}=\frac{3}{x + 2}$\n\nhow long did yumi spend picking up litter?\n\n1 hour 20 minutes\n3 hours 20 minutes\n4 hours\n6 hours

Answer

Explanation:

Step1: Cross - multiply the equation

$2(x + 2)=3x$

Step2: Expand the left - hand side

$2x+4 = 3x$

Step3: Solve for x

$4=3x - 2x$ $x = 4$

Step4: Find Yumi's time

Yumi's time is $x + 2$. Substitute $x = 4$ into $x + 2$, we get $4+2=6$ hours.

Answer:

6 hours