Question

The Jones family and the Henderson family each used their sprinklers last summer. The water output rate for the Jones family's sprinkler was 30 L per hour. The water output rate for the Henderson family's sprinkler was15 L per hour. The families used their sprinklers for a combined total of hours, resulting in a total water output of 750 L. How long was each sprinkler used?

Answer 1

16 hours 40 minutes

Explanation:

Rate = Volume/time

Rate of Jones = 30 L/hr

Rate of Henderson sprinklers = 15 L/hr

let volume of jones sprinklers be 'x' and volume of henderson sprinklers be 'y'

`(dx)/(dt)` = 30

dx = 30 dt (integrating both sides)

x=30t

Similarly,

`(dy)/(dt)` = 15

dy = 15 dt (integrating both sides)

y = 15t

Total volume of water is 750L, therfore;

x + y =750

30t + 15t = 750

t = 750/45

t = 16.667 hrs

or t = 16 hrs 40 mins