SOLUTION: HI! I REALLY LOVE SOLVING WORD PROBLEMS AND I LOVE MATH... I WOULD BE HAPPY TO KNOW THE SOLUTIONS FOR THE SAKE OF LEARNING IT.... THANK YOU 1.) VINCENT AND RICO CAN CEMENT A WALK

Question 155319: HI! I REALLY LOVE SOLVING WORD PROBLEMS AND I LOVE MATH... I WOULD BE HAPPY TO KNOW THE SOLUTIONS FOR THE SAKE OF LEARNING IT.... THANK YOU
1.) VINCENT AND RICO CAN CEMENT A WALK TOGETHER FOR 7 DAYS. RICO LEAVES TO WORK LEAVING VINCENT TO FINISH THE REST IN 5 DAYS MORE. HOW LONG WILL IT TAKE VINCENT TO DO THE JOB ALONE?

2.1) IT TAKES A SMALLER FAUCET 5 HOURS TO FILL THE RESERVOIR WHILE A BIGGER FAUCET ONLY 2 HOURS. IF BOTH FAUCETS ARE OPENED SIMULTANEOUSLY, IN HOW MANY HOURS WILL THE RESERVOIR BE FILLED?
2.2) IF AFTER ONE HOUR THE BIGGER FAUCET IS CLOSED LEAVING THE SMALLER FAUCET TO FILL UP THE RESERVOIR, AFTER HOW MANY HOURS WILL IT TAKE FOR THE SMALLER FAUCET TO FILL THE RESERVOIR?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.) VINCENT AND RICO CAN CEMENT A WALK TOGETHER FOR 7 DAYS.
RICO LEAVES TO WORK LEAVING VINCENT TO FINISH THE REST IN 5 DAYS MORE.
HOW LONG WILL IT TAKE VINCENT TO DO THE JOB ALONE?
---------
Together rate: 1/R + !/C = 1/7
Comment: Your 2nd sentence is missing some essential words.
=============================================================
2.1) IT TAKES A SMALLER FAUCET 5 HOURS TO FILL THE RESERVOIR WHILE A BIGGER FAUCET ONLY 2 HOURS. IF BOTH FAUCETS ARE OPENED SIMULTANEOUSLY, IN HOW MANY HOURS WILL THE RESERVOIR BE FILLED?
----------
Smaller Faucet DATA:
time = 5 hrs/job ; rate = (1/5) job/hr
--------------------
Larger Faucet DATA:
time = 2 hrs/job ; rate = (1/2) job/hr
--------------------------------------------
Together DATA:
time = x hrs/job ; rate = (1/x) job/hr
--------------------------------------------
EQUATION:
rate + rate = together rate
1/5 + 1/2 = 1/x
2x + 5x = 10
7x = 10
x = 10/7 = 1 3/7 hrs ( time for both to do the job together)
--------------------------------------------------------------------
2.2) IF AFTER ONE HOUR THE BIGGER FAUCET IS CLOSED LEAVING THE SMALLER FAUCET TO FILL UP THE RESERVOIR, AFTER HOW MANY HOURS WILL IT TAKE FOR THE SMALLER FAUCET TO FILL THE RESERVOIR?
--------
The larger faucet completes 1/2 of the job in one hour.
---------------
Smaller Faucet DATA:
rate = 1/5 job/hr
rate = (2/5) [(1/2)job/hr]
----------
EQUATION:
Let the time required to finish the job be "x".
time* rate = work done
x(2/5) = (1/2)
x = (1/2)(5/2) = 5/4 = 1 1/4 hr.
====================================
Cheers,
Stan H.

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