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Smart Math Time Speed Distance

[Smart Math] Time Speed Distance Problem 7

Here’s and example of a SMART MATH problem for TIME SPEED DISTANCE.

Time Speed Distance

Problem

If I walk to my office at 6 km/hr, I arrive 6 minutes early. If however, I walk at 4 km/hr, I arrive 4 minutes late. What is the distance that I walk to reach the office?

  1. 2 kms
  2. 2.5 kms
  3. 3 kms
  4. 4 kms
  5. 6 kms

The Usual Method

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Let the usual time taken to reach office be ‘t’ hours and distance be ‘4’ kms.

Hence, \frac{d}{6}=\left( t-\frac{6}{60} \right)hours and \frac{d}{4}=\left( t+\frac{4}{60} \right)hours

\therefore \frac{d}{6}+\frac{6}{60}=\frac{d}{4}-\frac{4}{60}

10d+6=15d-4

\therefore 5d=10

\therefore d=2kms

(Ans: 1)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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At 6 km/hr it takes \frac{1}{6}th of an hour to travel 1 km

At 4 km/hr it takes \frac{1}{4}th of an hour to travel 1 km

Hence, time difference is \frac{1}{4}-\frac{1}{6}=\frac{1}{12}hour = 5 minutes.

Actual difference in time = 10 minutes.

If difference in time = 5 minutes for 1 km,

For difference in time = 10 minutes, distance = 2 kms

(Ans: 1)

Estimated Time to arrive at the answer = 15 seconds.

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