SOLUTION: the Collins family and the Adams family each used their sprinklers last summer. The Collins family sprinklers was used for 15 hours. The Adams family sprinklers was used for 25 hou

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Question 1070248: the Collins family and the Adams family each used their sprinklers last summer. The Collins family sprinklers was used for 15 hours. The Adams family sprinklers was used for 25 hours. There was a combined total output of 1475 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 75 l per hour?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rate for Collins family =
+a%2F15+ L/hr
Let the rate for the Adams family =
+b%2F25+ L/hr
---------------------------------
Given:
(1) +a%2F15+%2B+b%2F25+=+75+ L/hr
(2) +a+%2B+b+=+1475+
----------------------------------
Multiply both sides of (1) by +75+
(1) +5a+%2B+3b+=+5625+
-----------------------------------
Multiply both sides of (2) by +3+
and subtract (2) from (1)
(1) +5a+%2B+3b+=+5625+
(2) +-3a+-+3b+=+-4425+
-------------------------
+2a+=+1200+
+a+=+600+
and
(2) +a+%2B+b+=+1475+
(2) +600+%2B+b+=+1475+
(2) +b+=+875+
---------------------------
Rate for Collins family:
+600%2F15+=+40+ L/hr
Rate for Adams family:
+875%2F25+=+35+ L/hr
---------------------------
check:
(1) +a%2F15+%2B+b%2F25+=+75+ L/hr
(1) +40+%2B+35+=+75+
(1) +75+=+75+
OK
check the math