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ch4aika [34]
3 years ago
5

the intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but with the outlet pipe open it takes 9 hour

s. How long would it take the outlet pipe to empty a full tank?
Mathematics
1 answer:
Leona [35]3 years ago
6 0

The outlet pipe will take 18 hours to empty the tank.

St<u>ep-by-step explanation:</u>

Number of hours taken by inlet pipe to fill the tank=6

work done by the inlet pipe in 1 hour=1/6

Number of hours taken by the inlet pipe to fill the tank with the outlet pipe open=9

work done by the inlet pipe in 1 hour with outlet  pipe open=1/9

we have to determine the time taken by the outlet pipe to empty the tank

The inlet and outlet pipe does the opposite work.

\\time\ taken\ by\ the\ outlet\ pipe\ to\ empty\ the\ tank=x\\work\ done\ by\ the\ outlet\ pipe\ in\ 1\ hour=1/x\\(1/6-1/x)9=1\\1/6-1/x=1/9\\1/x=1/6-1/9=3/54\\x=54/3=18

The outlet pipe takes 18 hours to empty the tank.

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A bus company took a tour bus on a ferry when there were 30 people aboard. The ferry charged the bus company $180. The following
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Problem: A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? How much does each person cost? Show this using y = mx + b form.

Solution:
Let x = the number of people on the bus
Let y = the total cost for the bus with its passengers to use the ferry.

Then, when there are 30 people on the bus (x = 30), the cost was $180 (y = 180). This means the point (x, y) = (30, 180).
Also, when there were 50 people on the bus, the cost was $220. So that is the point (50, 220).

You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope.

The slope of the line joining two points is the rise divided by the run. That means

m = (y2 - y1) / (x2 - x1)

So we put in the values of (30, 180) and (50, 220):

m = (220 - 180) / (50 - 30)
m = 40 / 20
m = 2.

The slope is 2. Now we can write it in the form y = mx + b, using 2 for m:

y = 2x + b.

This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 50 and y = 220:

220 = 2(50) + b
220 = 100 + b
b + 100 = 220
b = 120.

Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:

y = 2x + 120.

For the other questions, I can look at the equation I got. The y-intercept (b value) is $120. That means that we are adding $120 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.

Here's an example: if you had just 10 people on the bus, you'd pay $120 for the empty bus and $2 for each person. That's $20 for the people and $120 for the bus. That total is $140. Let's see if (10, 140) works in the equation we got:

y = 2x + 120
140 ?=? 2(10) + 120
140 ?=? 20 + 120
yes. 140 = 140. It does work.

Now you try it with your question.
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