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[Smart Math] Time Speed Distance Problem 2

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

Problem

If a man walks to his office at 3/4th of his usual rate, he reaches office 1/3rd of an hour later than usual. How much time does he usually take to reach his office?

1. 1/2 hour
2. 1 hour
3. 1/4 hour
4. 3/2 hours
5. 2/3 hour

The Usual Method

Assuming the distance between his home and office as ‘4’, his usual speed as ‘s’ and the usual time as ‘t’.

Hence, $t=\frac{d}{s}$

When s becomes 3/4 of s, t becomes $\frac{d}{\frac{3}{4}s}=t+\frac{1}{3}$

$\therefore t+\frac{1}{3}=\frac{d}{\frac{3}{4}s}$

$\therefore \frac{d}{s}+\frac{1}{3}=\frac{4d}{3s}$

$\therefore \frac{1}{3}=\frac{4d}{3s}-\frac{d}{s}$

$\therefore \frac{1}{3}=\frac{d}{3s}$

$\therefore \frac{d}{s}=1=t$

Hence usual time = 1 hour.

(Ans: 2)

Estimated Time to arrive at the answer = 60 seconds.