Question 221040
Suppose that a trip from the dormitory to the lake at 30 mi/h takes 12 min longer than the return trip at 48 mi/h. How far apart are the dormitory and the lake?


Let distance between dorm and lake be D


Since speed from dorm to lake is 30 mph, then time to get to lake = {{{D/30}}}


Since speed from lake to dorm is 48 mph, then time to get to dorm = {{{D/48}}}


Now, since it takes 12 more minutes to get from the dorm to the lake than it takes to get from the lake to the dorm, then it takes {{{12/60}}} of an hour, or {{{1/5}}} of an hour more, and we therefore have:


{{{D/30 - 1/5 = D/48}}}


8D - 48 = 5D ------- Multiplying by LCD, 240


8D - 5D = 48


3D  =  48


{{{D = 48/3}}} = {{{16}}} miles


Therefore, the dorm and the lake are {{{highlight_green(16)}}} miles apart.