<p>Let me give a few more solutions to the rate problem I presented earlier. Here is the problem again:</p>
<p>Joseph drove from home to work at an average speed of 30 miles per hour and returned home along the same route at an average speed of 45 miles per hour. If his total driving time for the trip was 3 hours, how many minutes did it take Joseph to drive from work to home?</p>
<p>(A) 135
(B) 72
(C) 60
(D) 50
(E) 30</p>
<p>We have already seen solutions to this problem using a “d=rt chart” and pckeller’s method of ratios. Here are a few more solutions:</p>
<p>Solution using Xiggi’s formula: Average Speed = 2(30)(45)/(30 + 45) =36
So Total Round Trip Distance = r<em>t =36</em>3 = 108
Distance from Work to Home = 108/2 = 54
Time from Work to Home = distance/rate = 54/45 = 1.2.</p>
<p>Finally multiply by 60 to convert to minutes. 1.2*60 = 72, choice (B).</p>
<p>Solution by starting with choice (C): Let’s start with choice (C). If it took Joseph 60 minutes (or 1 hour) to get from work to home, then the distance from work to home is d = 45 miles. This is the same as the distance from home to work. Therefore, the total time for Joseph to get from home to work would be t = d/r = 45/30 = 1.5 hours. But that means that the total trip only took 2.5 hours. So we can eliminate choices (C), (D), and (E). Since Joseph is traveling faster from work to home, it should take him less than half the time to get home. So the answer is less than 1.5 hours = 90 minutes. This eliminates choice (A), and therefore the answer is choice (B).</p>
<p>Solution by estimation: 3 hours is the same as 180 minutes. If John was travelling at the same rate for the whole trip, it would take him exactly half this time to get from work to home, 90 minutes. Since Jon is travelling a little faster on the way from work to home, the answer will be a little less than 90, most likely 72, choice (B).</p>