Observe equations (3) and (4). Are they linear equations? How do we solve them then? We can convert them into linear equations by substituting 1x= u and 1y = v Equation (3) becomes 80u + 120v = 1 (5) Equation (4) becomes 84u + 112v = 1 (6) L.C.M. of 80 and 84 is 1680. Using the elimination method,
Equation (3) × 21 (21 × 80)u + (21 × 120)v = 21 Equation (4) × 20 (20 × 84)u + (20 × 112)v = 201680u+2520v = 211680u+2240v = 20 Same sign for u, so subtract (-) (-) (-)280v = 1v = 1280 Substitute in equation (5) 80u + 120 × 1280 = 180u = 1 - 37 = 7 37- = 47 14 1201´ = u = 1407 80 So one man alone can finish the work in 140 days and one woman alone can finish thework in 280 days. Example-14. A man travels 370 km partly by train and partly by car. If he covers 250 km bytrain and the rest by car, it takes him 4 hours. But if he travels 130 km by train and the rest by car,it takes 18 minutes more. Find the speed of the train and that of the car. Solution : Let the speed of the train be x km. per hour and that of the car be y km. per hour. Also, we know that time = DistanceSpeed In situation 1, time spent travelling by train = 250x hrs. And time spent travelling by car = 120y hrs.