This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Define variables for the current ages. Let the current age of the father be F years. Let the current age of the son be S years. Step 2: Formulate equations based on the given conditions. According to the first condition, 10 years ago, the father's age was three times the son's age. Father's age 10 years ago: F - 10 Son's age 10 years ago: S - 10 So, we have the equation: F - 10 = 3(S - 10) F - 10 = 3S - 30 F = 3S - 20 (*) According to the second condition, 10 years from now, the father's age will be twice the son's age. Father's age 10 years from now: F + 10 Son's age 10 years from now: S + 10 So, we have the equation: F + 10 = 2(S + 10) F + 10 = 2S + 20 F = 2S + 10 (**) Step 3: Solve the system of equations to find the current ages. We have two expressions for F. Equate them: 3S - 20 = 2S + 10 Subtract 2S from both sides: 3S - 2S - 20 = 10 S - 20 = 10 Add 20 to both sides: S = 10 + 20 S = 30 The current age of the son is 30 years. Now substitute S = 30 into equation (**) to find F: F = 2(30) + 10 F = 60 + 10 F = 70 The current age of the father is 70 years. Step 4: Calculate the ratio of their current ages. The ratio of the father's current age to the son's current age is (F)/(S). (F)/(S) = (70)/(30) (F)/(S) = (7)/(3) The ratio of their current ages is 7:3. The ratio of their current ages is 7:3. Send me the next one 📸