An algebra problem by No Name

Algebra Level 1

Adam wants to go to his friend Jeff's house. Adam's house is in one corner of a square field whose length is 0.1 kilometers, and Jeff's is in the opposite corner of said field. If Adam walks at 5 kilometers per hour, is it faster for him to take the direct route through the field, or to walk along the sidewalk next to the field? By how many minutes? (Round to the hundredths.)

The direct route, 2 minutes The sidewalk, 2 minutes The sidewalk, 0.6 minutes The direct route, 0.6 minutes

1 solution

No Name
Aug 27, 2014

Since we know the field is 100 meters wide, the sidewalk route is 200 meters long (100 per side, 2 sides, 100*2). The direct route will take a little more work. We can use the Pythagorean Theorem to figure out the length. Both sides are 100, so:

${ 100 }^{ 2 }+{ 100 }^{ 2 }={ c }^{ 2 }\\ 10000+10000={ c }^{ 2 }\\ 20000={ c }^{ 2 }\\ \sqrt { 20000 } =\sqrt { { c }^{ 2 } }$

From here, we will evaluate both expressions with the time formula, $t=\frac { d }{ r }$ .

$Sidewalk\\ t=\frac { d }{ r } \\ t=\frac { 200 }{ 5000 } \\ t=0.04\quad hours,\quad or\quad 2.4\quad minutes\\ \\ Direct\quad route\\ t=\frac { d }{ r } \\ t=\frac { 141.42 }{ 5000 } \quad \\ t=0.03\quad hours,\quad or\quad 1.8\quad minutes$

Therefore, the direct route is faster by 0.6 minutes.

An algebra problem by No Name

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