a production manager tests 10 toothbrushes and finds that their mean lifetime is 450 hours. she then designs a sales package for
2 answers:
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Answer:
Pipe 1 alone fills a tank in 10 min
Pipe 2 alone fills the tank in 20 min
If both are turned on together, how long will it take to fill the tank???
Pipe 1 fills at the RATE of 1/10th tank per min
Pipe 2 fills at the RATE of 1/20th tank per min
Pipe 1 + Pipe 2 fills at the rate of 1/10+1/20 or 3/20th tank per min
Let x= time to fill the tank
(3/20)(x)=1 Where 1 denotes a full tank (Multiply both sides by 20)
3x=20
x=6 2/3 min----------both working together
NOW YOUR PROBLEM
Let x= amount of time for smaller pipe to fill the tank
Then (x-5)=amount of time for larger pipe to fill the tank
NOW HERE'S WHERE THE RECIPROCAL COMES IN:
The smaller pipe fills the tank at the RATE of 1/x cu units per min
The larger tank fills the tank at the RATE of 1/(x-5) cu units per min
Together, they fill the tank at the rate of 1/x+(1/(x-5)) cu units per min
But now we are told that together the fill the tank in 11 1/9 minutes. so our equation to solve is:
(1/x+(1/(x-5))(11 1/9)=1 where 1 denotes a full tank. In fact, in each of the above reciprocals, the 1 denotes a full tank.
So, dividing both sides by 11 1/9, we get:
1/x+(1/(x-5)=1/(11 1/9)-------------- which is your equation
I assume that you have no problems solviing this eq.
Hope this helps----ptaylor
Step-by-step explanation:
Answer:
The distance from the shoreline from P the pipe from the island will reach land in order to minimize the total construction cost is 0 m, or the pipe should be routed to the point P
Step-by-step explanation:
We note that, cost to lay pipe in water = 2.3 × cost to lay pipe on land
Distance of the small resort on the island from point p on the shoreline = 3 miles
Location of the closest source of fresh water is 10 miles along the shoreline from p
∴ The small resort, the point p and the closest source of the fresh water on the shoreline together form a right triangle with sides
Height = 3 miles
Base = 10 miles and
Hypotenuse =
To find the cost of laying the pipeline by the various route, we multiply the water routes by 2.3 and the land routes by 1 and we get
Costs:
Height = Water route = 2.3 × 3 miles = 6.9
Base = Land route = 1 × 10 miles = 10
Hypotenuse = Water route = 2.3 × 10.44 miles = 24.012
Therefore, the two routes are either
10 miles to point p and 3 miles across the water to the resort with a cost = 10 + 6.9 = 16.9 or
Directly to the small resort through 10.44 miles across the water with cost = 24.012
Therefore, to minimize cost, the pipe should come from the resort to P from there to the fresh water source.
That is the distance from the shoreline from P the pipe from the island will reach land in order to minimize the total construction cost = 0 m.