Question

It took Charles 2 hours to reach a cafe that is 8 miles from his house. He returned to his house at half his initial speed. What is the total time taken by Charles for the round trip?

• A. 4 h
• B. 8 h
• C. 2 h
• D. 6 h

Answer 1

The correct option is B 8 h


Distance from house to cafe = 8 mi
Time taken to reach the cafe = 2 h
Speed at which Charles reached the cafe = slope of the line from the house to the cafe
$=\frac{\text{change in y-coordinate}}{\text{change in x-coordinate}}$
$=\frac{8-0}{2-0}$
$=\frac{8}{2}$
$=4$ mi per h

Let the time taken to reach the house from the cafe be $x.$
Speed at which Charles reached the house = slope of the line from the cafe to the house
$=\frac{\text{change in y-coordinate}}{\text{change in x-coordinate}}$
$=\frac{0-8}{x-2}$
$=\frac{-8}{x-2}$ mi per h (The negative sign indicates the slope is decreasing.)

Speed at which Charles reached his house $=\frac{1}{2}\times$ speed at which Charles reached the cafe
$=\frac{1}{2}\times 4$
$=2$ mi per h
Slope of the line from the cafe to house $=-2$ (The negative sign indicates the slope is decreasing.)
So, $-2=\frac{-8}{x-2}$
$\Rightarrow -2(x-2)=-8$
Dividing both sides by $-2,$
$\Rightarrow x-2=4$
$\Rightarrow x=6h$

Total time Charles took for the round trip $=2+6=8h$