Question

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?

Answer 1

1650 miles

Explanation:

Answer 2

`v_1=60mph\\ v_2=50mph\\ v_3=55mph\\ t_1- time\ needed\ to\ travel\ from\ X\ to\ Y\ at\ v_1\ and\ return\ with\ v_2\\ t_2- time\ needed\ to\ travel\ from\ X\ to\ Y\ at\ v_3\\\\ t_1-0,5h=t_2\\ s-travelled\ distance\\ v=(s)/(t)\\ v*t=s\\ t=(s)/(v)\\ (0,5s)/(60)+(0,5s)/(50)-0,5=(s)/(55)\\\\ (1)/(120)s+(1)/(100)s-(1)/(55)s=(1)/(2)\\ (1)/(6600)s=(1)/(2)\\ s=3300miles\\ Distance\ from\ town\ X\ to\ town\ Y\ is 1650miles.`