<p>Ok so this problem has been bugging me for awhile. The Princeton Review explanation was confusing and did not make any logical sense at all.</p>
<p>Ray and Jane live 150 miles apart. Each drives towards the other's house along a straight road connecting the two, Ray at a constant rate of 30mph and Jane at a constant rate of 50mph. If Ray and Jane leave their houses at the same time, how many miles are they fromRay's house when they meet? </p>
<p>A) 40
B) 51.5
C) 56.25
D) 75
E) 93.25</p>
<p>For some reason, I always have trouble with time distance rate problems. Not like those easy ones, but the ones that have extra information missing. Like the one above. Idk that's just how I feel about these problems.</p>
<p>Assume the origin is at Ray’s house. Let x be Ray’s position from his house as he drives to meet Jane. x = vt where v is Ray’s speed. So x = 30t.</p>
<p>Jane’s house is at position 150. Jane drives toward Ray’s house. Let y be Jane’s position from Ray’s house as she drives to meet him. y = 150 - ut where u is Jane’s speed. When they meet x = y. So 30t = 150 - 50t or t = 150/80 = 15/8. So x = (30)(15/8) = 450/8 = 56.25 miles.</p>
<p>Here’s one other way that contains a useful trick (and no algebra):</p>
<p>First you have to notice that since they travel the same amount of time, their distances will be proportional to their speeds. So the 150 miles of distance will be split into two parts that have the ratio 30:50 with John’s being the smaller one.</p>
<p>So now the question boils down to dividing 150 into two parts in a 3:5 ratio. That is a ratio skill that comes in handy in other settings as well: take 150, divide it by 8 (because 3 parts to 5 parts means that there are 8 parts total). Then multiply by 3 to get John’s share of the distance. So it’s (150/8) x 3 = 56.25.</p>
<p>Make it simple: Ray travels 3/8 of the 150 miles, Jane the other 5/8. 3/8 of 150 mi is 56.25. Choice C.</p>
<p>The Princeton review "Joe Blogs strategy is mediocre, since you’ll be able to narrow the answer down to B and C, but simple logic will get you the right answer.</p>