The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $8.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?  Answers:  A) $ 8.40  B) $ 5.10  C) $ 5.30  D) $ 5.50  E) $ 5.60

Rationale: "i tried using time / rate approach : - initial price difference = 8.80 - 3.20 = 5.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 5.6 = t ( 5.4 x ) - > t = ( 5.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 5.6 / 5.4 = 8.4 answer a ."
Answer: A