# Puzzle on Distance Walked to Office

## Distance Walked to Office Puzzle

Solve the Puzzle on Distance walked to the office.

Alex’s friend Grace drops her off at work every day in the morning, but she can’t resist but drop her off at home in the evening. The puzzle is about the distance walked to the office puzzle.

Premise – Every day, he walks home from work. However, after a few days, her boss offered her a metro pass as a reward for her hard work. She now only has to walk from her office to a local metro station and from a nearby metro station to her home.

Rule – She walks 1/8th of the distance she did before by following this exercise. Assuming she walks at the same pace every time, she arrived home 15 minutes earlier than normal.

Objective – If the time she traveled in the metro (apart from her walking) is 5 minutes, what is the total amount of time she used to walk in her older routine (without taking the metro)?

### Solution

Let the distance she walks in her new routine from her office to a nearby station be ‘y’ and the time she takes to be $‘t_{1}’$ and the distance from a station nearby to her home to her home be ‘z’ and the time he takes to be $‘t_{2}’$.

She walks 1/8th times less than before taking the new routine, which implies

x- $\frac{x}{8}$ = z+y ————–{1}

=> distance = speed * Time

=>x = v * t

=>y = v * $‘t_{1}’$

=>z = v * $‘t_{2}’$

From equation {1}

= $\frac{7}{8}$ (v*t) = v* $‘t_{1}’$+ v* $‘t_{2}’$

= $\frac{7}{8}$ (t) = t1 + t2 ————-{2}

She reached home 15 minutes earlier, which means

= > t-15 = $t_{2}$ + $t_{3}$ + Time taken in the metro

=> t-15 = $t_{2}$+ $t_{3}$ + 5

From equation {2}

=> t-15=$\frac{7}{8}$t+5

By solving the above equation, we get : t=160

Therefore, she used to walk 160 minutes every day.

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