Question 1188476
<br>
The first tutor used a standard formal algebraic solution method but used the wrong total travel time; I'm sure she will see this note and fix her response.<br>
The second tutor used a magic formula which is well worth remembering, since it appears in a large number of similar problems:<br>
The average speed for traveling from A to B and back at speeds of x and y is<br>
{{{(2xy)/(x+y)}}}<br>
Here is another informal way to solve the problem quickly, if formal algebra is not required.<br>
The ratio of the two speeds is 40:60 = 2:3, and the distances are the same, so the ratio of times at the two speeds is 3:2.<br>
So 3/5 of the total travel time of 6 hours was at 40mph, and 2/5 was at 60mph.  Using either of those facts gives the distance:<br>
3/5 of 6 hours at 40mph: (3/5)(6)(40) = 144 miles
2/5 of 6 hours at 60mph: (2/5)(6)(60) = 144 miles<br>