Ace Transport has acquired two trucks to carry different types of cargo. One costs $70,000; the other costs $52,000. The company expects that the first will last 165,000 miles, after which it can be sold for salvage for about $4,000. The other will fetch the same salvage price, but will last 200,000 miles. The two trucks convoy together, so they always show the same mileage readings. If the value of each truck declines at different constant rates for every mile driven, at what mileage reading will the residual values of the two trucks be equal?	Select the correct option:  A) 87,500 miles  B) 100,000 miles  C) 107,750 miles  D) 112,500 miles  E) The residual values will never be equal.
Truck 1 : 70,000 = m1 * 165,000 + 4,000 , where m1 is the depreciation $ per mile   Solve for m1 = 0.4   So the depreciation line for Truck 1 is y = 0.4 x + 4,000 , where y is in dollars and x is in mileage.   Similarly for Truck 2 : 52,000 = m2 * 200,000 + 4,000   and this gives m2 = 0.24   and similar line for Truck 2 is y = 0.24 x + 4,000.   The question is where values are same, and in terms of the equation, it's where the two depreciation lines meet.   so solve for x, 0.4 x + 4,000 = 72,000   0.24x + 4,000 = 52,000   gives x = 112,500,   ANSWER:112,500 miles
<result>D</result>
Ace Transport has acquired two trucks to carry different types of cargo. One costs $70,000; the other costs $52,000. The company expects that the first will last 165,000 miles, after which it can be sold for salvage for about $4,000. The other will fetch the same salvage price, but will last 200,000 miles. The two trucks convoy together, so they always show the same mileage readings. If the value of each truck declines at different constant rates for every mile driven, at what mileage reading will the residual values of the two trucks be equal?