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Speed Distance Time: Walking and Driving to Office

XAT 2016 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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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 1km, he reached a temple when his wife called to say that he can now take the car. Pradeep figure 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.

  1. A.

    1

  2. B.

    7/3

  3. C.

    9/7

  4. D.

    16/7

  5. E.

    16/9

Answer

C

Explanation

Let walking speed = ww, driving speed = 8w8w. Distance from home to temple = 1 km. Let distance from temple to office = xx km. Option 1: Continue walking to office from temple: Time = xw\frac{x}{w}. Option 2: Walk back home and drive to office: Time = 1w+1+x8w\frac{1}{w} + \frac{1+x}{8w}. Equating both times: xw=1w+1+x8w  ⟹  8x=8+1+x  ⟹  7x=9  ⟹  x=97 km.\frac{x}{w} = \frac{1}{w} + \frac{1+x}{8w} \implies 8x = 8 + 1 + x \implies 7x = 9 \implies x = \frac{9}{7} \text{ km.}

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