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# [Smart Math] Time Speed Distance Problem 4

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

### Problem

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

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

$t_{1}-t_{2}=2+2=4$minutes

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

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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