Alex’s friend Grace drops her every day to work in the morning to her office, but cannot help to drop her back home in the evening. ?he walks back home from work every day . But after a few days, As a reward of her sincerity in work, her boss offered her a metro pass. Now she needs to walk only from her office to a nearby metro station and from a station nearby her house to her house . Following this routine, she walks 1/8th times less than before. Assume that she always walks with the same speed, she reached home 15 minutes earlier than usual. 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 metro)?
Solution:
Let the distance she used to walk from work to her home be ‘x’ and the time take be ‘t’
Let the distance she walks in her new routine from her office to a nearby station be ‘y’ and the time she takes be ‘t1’ and the distance from a station nearby her home to her home be ‘z’ and the time he takes be ‘t2’
She walks 1/8th times less than before taking the new routine, which implies
x-x/8 = z+y ————–{1}
distance = speed * Time
x = v * t
y = v * t1
z = v * t2
From equation {1}
7/8 (v*t) = v*t1 + v*t2
7/8(t) = t1 + t2 ————-{2}
She reached home 15 minutes earlier, which means
t-15 = t2 + t3 + Time taken in the metro
t-15 = t2 + t3 + 5
From equation {2}
t-15=7/8t+5
By solving the above equation, we get
t=160
Therefore, she used to walk 160 minutes everyday.
This puzzle is contributed by Harika Mulumudi.