a.Patrice by himself can paint 4 rooms in 10 hours, if he hires april to help th
ID: 3102860 • Letter: A
Question
a.Patrice by himself can paint 4 rooms in 10 hours, if he hires april to help they can do the same job in 6 hours. if he lets april work alone how long will it take her to paint 4 rooms?
b. a pond is enclosed by a wooden deck that is 3 ft wide. the deck surrounding the fence is 100 ft long. a) is the pind is a square what are the dimensions b) if the pond is a rectangle, and the length of the pond is to be 3 times its width, what are its dimensions? c) if the pond is circular what are its diameter? d)which pond has the most area
c. the cooling system of a certain foreign made car has a capacity of 15 liters. if the system is filled with a mixture of 40% antifreeze, how much of this mixture should be drained and replaced by pure antifreeze so that the system is filled with a solution this is 60% antifreeze
Explanation / Answer
a) Patrick's speed is 4rooms/10hrs=0.4room/hr April's speed is 4room/(x)hrs=(4/x)room/hr together they paint 4rooms in 6hrs that is: Patrick's speed*(6hrs)+April's speed*(6hrs)=4rooms (4/10)(6)+(4/x)(6)=4 hence x=1/(1/6-1/10)=60/4=15 hence April will paint 4rooms by herself in 15hrs b)1.if the pond is a square of side a, then its perimeter 4a=100ft, so a=25ft 2.if the pond is a rectangle, and the length of the pond is to be 3 times its width, then its perimeter 2*(l+w)=2*(3w+w)=8w=100ft, so w=12.5ft and l=3w=37.5ft 3. if the pond is circular with diameter D, then its perimeter is (pi)*D=100ft, so D=31.83ft 4. let's compute the areas: -square of side a=25ft; area=25*25=625 ft^2 -rectangle of length l=37.5ft and width w=12.5ft; area=37.5*12.5=486.75 ft^2 -circle with diameter D=31.83ft; area=(1/4)*(pi)*(31.83*31.83)=795.75 ft^2 the largest area is the circular area. c) we want x=amount of pure antifreeze added; the equation to solve is: total amount of antifreeze needed= amount of antifreeze left in the system + amount of pure antifreeze added 0.6*15=0.4(15-x)+x which gives 0.6x= 0.2*15 or x=5liters
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