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TIFR CSE 2018 | Part A | Question: 4

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The distance from your home to your office is $4$ kilometers and your normal walking speed is $4$ Km/hr. On the first day, you walk at your normal walking speed and take time $T_1$  to reach office. 

On the second day, you walk at a speed of $3$ Km/hr from $2$ Kilometers, and at a speed of $5$ Km/hr for the remaining $2$ Kilometers and you take time $T_{2}$ to reach office.

On the third day, you walk at a speed of $3$ Km/hr for $30$ minutes, and at $5$ Km/hr for the remaining time and take time $T_{3}$ to reach office.

What can you say about the ordering of $T_{1},T_{2}$ and $T_{3}$

  1. $T_{1}>T_{2}$ and $T_{1}<T_{3}$
  2. $T_{1}=T_{2}=T_{3}$
  3. $T_{1}<T_{2}$ and $T_{1}>T_{3}$
  4. $T_{1}=T_{2}$ and $T_{1}<T_{3}$
  5. $T_{1}<T_{2}$ and $T_{1}=T_{3}$
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$T_1=\frac{4 km}{4km/hr}=1 hr$

$T_2=\frac{2 km}{3km/hr}+\frac{2 km}{5 km/hr}=1.067 hr$

Distance travelled in $30$ minutes$=3*\frac{30}{60}=\frac{3}{2} km$

$T_3=\frac{\frac{3}{2}km}{{3}km/hr}+\frac{4-\frac{3}{2}km}{{5}km/hr}=1 hr$

$T_1=T_3 $ and $T_1<T_2$
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