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Question 99

A person travels from P to Q at a speed of 60 kmph and returns at a speed of 45 kmph If total time taken is $$3\frac{1}{2}$$ hours then the distance (in kms) between P and Q is

Solution

Let the distance between P and Q be D km.

Total time = $$3\frac{1}{2}$$ hours = 3.5 hours

According to the problem, $$\frac{D}{60}+\frac{D}{45}=3.5$$

$$\Rightarrow$$ $$\frac{1}{15}\left(\frac{D}{4}+\frac{D}{3}\right)=3.5$$

$$\Rightarrow$$ $$\frac{1}{15}\left(\frac{7D}{12}\right)=3.5$$

$$\Rightarrow$$ D = 90 km

$$\therefore\ $$Distance between P and Q = 90 km

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