Smart Math Time Speed Distance

[Smart Math] Time Speed Distance Problem 4

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

Time Speed Distance


If I walk at 3 mph (miles per hour), I miss the train by 2 minutes. If however, I walk at 4 mph, I reach the station 2 minutes before arrival of the train. How far do I walk to reach the station?

  1. \frac{3}{4} mile
  2. \frac{4}{5} mile
  3. 1 mile
  4. \frac{5}{4} miles
  5. \frac{4}{3} miles

The Usual Method

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Let the distance between home and station be ‘4’ miles. Hence, time taken to cover d miles at 3 mph, t_{1}=\frac{d}{3} hours.

Similarly, time taken at 4 mph, t_{2}=\frac{d}{4} hours


Hence, \frac{d}{3}-\frac{d}{4}=\frac{4}{60}hours

\therefore \frac{d}{12}=\frac{4}{60}

\therefore d=\frac{4}{5}mile

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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To cover 1 mile @ 3 mph, it takes 20 minutes

To cover 1 mile @ 4 mph, it takes 15 minutes

Hence, time gap = 20 – 15 = 5 minutes

Thus for a distance of 1 mile, time gap = 5 minutes

Hence, a time gap of 4 minutes (2 + 2), distance is correspondingly \frac{4}{5}mile.

(Ans: 2)

Estimated Time to arrive at the answer = 10 seconds.

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