Question

A motorist travelled from town $A$ to town $B$ ar an average speed of $54km/hr$. On his return journey, his average speed was $60kmph$. If the total time taken is $9\frac{1}{2}$ hours, find the distance between the two towns .

Answer 1

Given that,

travelled averageSpeed$=54km/h$

return average speed$=60km/h$

Total time taken $=9\frac{1}{2}=\frac{19}{2}$hours.

Let total distance $x$.

$\begin{array}{c}\frac{x}{54}+\frac{x}{60}=\frac{19}{2}\\ \frac{10x+9x}{540}=\frac{19}{2}\\ 19x=\frac{540\times 19}{2}\end{array}$

$x=\frac{540}{2}=270$km/h

Then,

We get total distance is $270km/h$