question that needs an answer, please

Question

The Roberts family and the Choi family each used their sprinklers last summer. The water output rate for the Roberts family's sprinkler was 40L

 per hour. The water output rate for the Choi family's sprinkler was 20L

 per hour. The families used their sprinklers for a combined total of 75

 hours, resulting in a total water output of 2200L

. How long was each sprinkler used?

Answer 1

Here's the substitution method:

R = 40 L/hr

C = 20 L/hr

Tc + Tr = 75 hrs.

Water usage = 40(Tr) + 20(Tc) = 2200

but Tr= 75 - Tc

40(75 - Tc) + 20(Tc) = 2200

3000 - 40(Tc) + 20(Tc) = 2200

800 = 20(Tc) → Tc = 40 hrs

So Tr = 75 - 40 = 35 hrs

Answer 2

r + c = 75

multiply by 40

40r+40c =40(75)=3000

subtract

40r +20c = 2200

to get

40c-20c =3000-2200

20c = 800

c =800/20 = 40 hours for choi family

r = 75-40 = 35 hours for roberts family

40(35)+20(40)

= 1400+800=2200

Answer 3

Let R = Roberts hours and C=Choi hours

R + C =75

40R + 20C = 2200

Divide the 2nd equation by 20, then subtract to eliminate the C.