Question

If a scooterist drives at the rate of $24$kmphr , he reaches his destination $5$ minutes late,and if he drives at the rate of $30$kmphr, he reaches his destination $4$ minutes earlier.Find how far is his destination.

Answer 1

Let his destination be $x$kmphr

If he drives at the rate of $24$kmphr, time taken by him$=\frac{distance}{speed}=\frac{x}{24}$

Correct time$=\frac{x}{24}-\frac{5}{60}$ ......$\left(1\right)$

If he drives at the rate of $30$kmphr, time taken by him$=\frac{x}{30}$

Correct time$=\frac{x}{30}+\frac{4}{60}$ ......$\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

$\frac{x}{24}-\frac{5}{60}=\frac{x}{30}+\frac{4}{60}$

$\Rightarrow \frac{x}{24}-\frac{x}{30}=\frac{4}{60}+\frac{5}{60}$

$\Rightarrow \frac{5x-4x}{120}=\frac{9}{60}$

$\Rightarrow x=\frac{3}{20}\times 120$

$\therefore x=18$

Hence, the destination is $18$kmphr