Lesson The Robinson family and the Sanders family each used their sprinklers last summer

The Robinson family and the Sanders family each used their sprinklers last summer

Problem 1

Let x be the time (in hours) of use sprinklers by the Robinson family, and

let y be the time (in hours) of use sprinklers by the Sanders family.



Then from the condition, you have these two equations in two unknowns

  x +   y =   55    (1)
25x + 20y = 1250    (2)


Express  x = 55 - y  from equation (1)   and substitute it into the equation (2). You will get

25*(55-y) + 20y =1250.


Simplify and solve it for y:

1375 - 25y + 20y = 1250.

-5y = 1250 - 1375

-5y = -125.

y =  = 25.


Then x = 55 - y = 55 - 25 = 30.


Answer. 30 hours of use by the Robinson family, and 25 hours of use by the Sanders family.

Check.  30*25 + 25*20 = 1250.   Correct !

Let x be the time (in hours) of use sprinklers by the Robinson family.

Then the time of use sprinklers by the Sanders family is (55 - x) hours.


25x + 20*(55 - x) = 1250,

25x + 1100 - 20x = 1250,

5x = 1250 - 1100,

5x = 150.

x =  = 30.

55 - 30 = 25.


Answer. Same as in the Solution 1:  30 hours of use by the Robinson family, and 25 hours of use by the Sanders family.

Problem 2

Let x = the water output rate for the Taylor family' sprinklers, in liters per hour.


Then the water output rate for the Johnson family' sprinklers is (55-x).


The combined total output water equation is

    30x + 20*(55-x) = 1450 liters.


Isolate the terms with x

    30x - 20x = 1450 - 20*55


and find x

    x =  = 35 liters per hour.


ANSWER.  Taylor family' sprinklers output rate is 35 L/hour.

         Johnson family' sprinklers output rate is 55-35 = 20 L/hour.