Question

Pradeep could either walk or drive to office. The time taken to walk to the office is $8$ times the driving time. One day, his wife took the car making him walk to office. After walking $1$ km, he reached a temple when his wife called to say that he can now take the car. Pradeep figures that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office.

• A. 1
• B. 7/3
• C. 9/7
• D. 16/7
• E. 16/9

Hint:

In time–distance problems with ratios, always express walking and driving speeds relative to each other. Setting up two time equations for alternative routes and equating them directly gives the required distance.

Answer 1

The Correct Option is C

Step 1: Define variables.
Let distance from home to office $= D$ km.
Let driving speed $= v$, so walking speed $= v/8$ (since walking takes 8 times longer). Step 2: Walking and driving times.
- Time to drive $D$ km $= D/v$.
- Time to walk $D$ km $= 8D/v$. Step 3: Analyze the two alternatives at the temple.
At the temple, distance covered $=1$ km (walking). Distance remaining to office $= D-1$. \underline{Case 1: Continue walking to office.}
Time $= \dfrac{D-1}{v/8} = \dfrac{8(D-1)}{v}$. \underline{Case 2: Return home (1 km back) and drive to office.}
- Walking back $1$ km: time $= \dfrac{1}{v/8} = \dfrac{8}{v}$.
- Driving $D$ km: time $= D/v$.
Total time $= \dfrac{8}{v} + \dfrac{D}{v} = \dfrac{D+8}{v}$. Step 4: Equating times (given condition).
\[ \frac{8(D-1)}{v} = \frac{D+8}{v} \] \[ 8D - 8 = D + 8 \] \[ 7D = 16 \;\;\Rightarrow\;\; D = \frac{16}{7}. \] Step 5: Distance from temple to office.
Temple is $1$ km from home, so remaining distance $= D - 1 = \frac{16}{7} - 1 = \frac{9}{7}\ \text{km}. \] \[ \boxed{\tfrac{9}{7}\ \text{km}} \]