Solve using algebra. Say that a husband andwife are driving to her mother’s hous
ID: 3090292 • Letter: S
Question
Solve using algebra. Say that a husband andwife are driving to her mother’s house. They have anappointment with a marriage counselor en route. After some timepasses, the wife asks, “How far are we from our house?”The husband replies, “Half as far as from here toPollyanna’s office.” A while after the appointment,they are 200 miles from where the wife asked her first question:“How far are we from Mother’s house?” The husbandtakes advantage of this golden opportunity and responds, “ Itold you already: Half as far from here to Pollyanna’soffice.” How far apart are the two houses?
Explanation / Answer
X = distance when wife asks the firsttime HO = distance from Home to Office Y = distance when wife asks the second time OM = distance from Office to Mothers HM = distance from Home to Mothers 1 We know that X = (1/3)*HO, which is the first timethe wife asks her question. Therefore, the distance from X tothe Office = (2/3)*HO, since the two distances must equal HO. 2 We also know that Y = (2/3)*OM, which is the secondtime the wife asks her question. 3 Finally, we know that the distance between X and Yis 200 Miles. Now we can solve the problem. The distance between X and Y can be thought of asthe distance from point X to the Office, plus the distance from theOffice to point Y. From (1) and (2) and (3) above: (2/3)*HO + (2/3)*OM = 200 (3/2) * [(2/3)*HO + (2/3)*OM] = (3/2) * 200 HO + OM = 300 HM = 300