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| 1. |
Place A and B 100km apart on a highway. One car starts from Bat the same time if the car |
| Answer» Let the speeds of the cars from A and B be x km/hr and y km/hr respectively.Case I When the two cars move in the same direction:In this case, let them meet at M after 5 hoursThen, AM = 5x km.And, BM = 5y km.{tex}\\therefore{/tex} AM -BM = AB{tex}\\Rightarrow{/tex} 5x - 5y = 100{tex}\\Rightarrow{/tex} 5(x - y) = 100{tex}\\Rightarrow{/tex} x - y = 20 ...............(i)Case II When the two cars move in the opposite directions:Let one car move from A to B and let the other move from B to A.Let them meet at N after 1 hour.Then, AN = x km and BN = y km.{tex}\\therefore{/tex} AN + BN = AB{tex}\\Rightarrow{/tex} x + y = 100. ............. (ii)Adding (i) and (ii), we get(x - y) + ( x + y) = 100 + 20{tex}\\Rightarrow{/tex} x - y + x + y = 120{tex}\\Rightarrow{/tex} 2x = 120{tex}\\Rightarrow{/tex} x = 60.Putting x = 60 in (ii), we getx+ y = 100{tex}\\Rightarrow{/tex} 60 + y = 100{tex}\\Rightarrow{/tex} y= 100 - 60{tex}\\Rightarrow{/tex} y = 40.So, x = 60 and y = 40Hence , speed of the car from A = 60 km/hr,and speed of the car from B = 40 km/hr | |