Question 1148884
<br>
Certainly you should understand the method for setting up the problem for solving by formal algebra, as shown in the response from the other tutor.<br>
However, if a quick solution by any means is allowed (or desirable, as in a timed competitive exam), then some logical trial and error can get you to the answer much faster than the formal algebra.<br>
(1) The total distance is 400 miles; the total time is 10 hours.  So the average rate is 40mph.<br>
(2) The two rates are not the same, so one of them is greater than 40mph and the other is less.  And the difference between the two rates is 9mph.<br>
(3) The total driving time is (exactly) 10 hours.  That means the two rates a and b must be "nice" numbers, satisfying 200/a + 200/b = 10.<br>
The two "nicest" numbers that are either side of 40 and have a difference of 9 are 36 and 45; so try them....<br>
{{{200/45+200/36 = 40/9+50/9 = 90/9 = 10}}}<br>
Done....!