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

**Problem**

**Problem**

A and B have to go from X to Y which are at a distance of 230 kms from each other. A drives at a constant speed of 100 kms/hr for the first 115 kms and then at an average speed of 50 kms/hr for the remaining distance. B starts with an initial speed of 50 kms/hr at X and drives with constant acceleration such that when he reaches Y, his speed is 100 kms/hr. Which of the following statement is true?

- A reaches Y first
- B reaches Y first
- A and B reach Y together
- Cannot calculate from given data
- None of these

**The Usual Method**

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A covers half of the distance at 100 kms/hr and the remaining half at 50 kms/hr. Hence average speed of A = 66.67 kms/hr

Average speed of B for the whole journey = 75 kms/hr

Average speed of B > Average speed of A,

B will reach Y before A does.

**(Ans: 2)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Note that speed of B follows Arithmetic mean and that of A follows Harmonic mean.

We know that for a given set of numbers, Harmonic Mean is always < Arithmetic Mean

Hence speed of A < speed of B, so B reaches Y before A.

**(Ans: 2)**

*Estimated Time to arrive at the answer = 10 seconds.*

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