> > A man travels from Town X to Town Y at an average rate of 60 mph and returns at an average rate of 50 mph.

# A man travels from Town X to Town Y at an average rate of 60 mph and returns at an average rate of 50 mph.

## He takes a 1/2 hour longer than he would take if he made the round ...

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### A man travels from Town X to Town Y at an average rate of 60 mph and returns at an average rate of 50 mph.

He takes a 1/2 hour longer than he would take if he made the round trip at an average of 55 mph.
What is the distance from Town X to Town Y?

$$v_1=60mph\\ v_2=50mph\\ v_3=55mph\\ t_1- timeeeded\ to\ travel\ from\ X\ to\ Y\ at\ v_1\ and eturn\ with\ v_2\\ t_2- time eeded\ to\ travel\ from\ X\ to\ Y\ at\ v_3\\\\ t_1-0,5h=t_2\\ s-travelled\ distance\\ v=\frac{s}{t}\\ v*t=s\\ t=\frac{s}{v}\\ \frac{0,5s}{60}+\frac{0,5s}{50}-0,5=\frac{s}{55}\\\\ \frac{1}{120}s+\frac{1}{100}s-\frac{1}{55}s=\frac{1}{2}\\ \frac{1}{6600}s=\frac{1}{2}\\ s=3300miles\\ Distance\ from\ town\ X\ to\ town\ Y\ is 1650miles.$$