The Aoki family and the Watson family each used their sprink

The Aoki family and the Watson family each used their sprinklers last summer. The water output rate for the Aoki family\'s sprinkler was 20L per hour. The water output rate for the Watson family\'s sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 900L. How long was each sprinkler used?


Aoki ____ Hours?

Watson______Hours?

Solution

Let the time for which the Aoki family and the Watson family used their sprinklers be x and y hours respectively. Then x+y = 50…(1). Further, the water outputs in the sprinkler of the Aoki family and the Watson family were 20x L and 15y L respectively so that 20x+15y = 900 or,on dividing both the sides by 5, we get 4x+3y = 180…(2). Now, on multiplying both the sides of the 1^st equation by 3, we get 3x+3y =150…(3). Further, on subtracting the 3^rd equation from the 2^nd equation, we get 4x+3y-3x-3y = 180-150 or, x = 30. Then, on substituting x = 30 in the 1^st equation, we get 30+y = 50 or, y = 50-30 = 20. Thus, last summer, the Aoki family and the Watson family used their sprinklers for 30 hours and 20 hours respectively.