The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $6.80. 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?	Choose the correct choice from the following answers
A) $ 4.50  B) $ 5.10  C) $ 5.30  D) $ 5.50  E) $ 6.50

Rationale: "i tried using time / rate approach : - initial price difference = 6.80 - 3.20 = 3.60 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 , 3.6 = t ( 5.4 x ) - > t = ( 3.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 3.6 / 5.4 = 6.5 answer e ."
Answer: E