Solution
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To convert minutes to hours, you need to know the basic time conversion factor: there are 60 minutes in one hour. This means that to convert minutes to hours, you divide the number of minutes by 60.
Here is a step-by-step solution to convert 160 minutes to hours:
Here is a step-by-step solution to convert 160 minutes to hours:
Here is a step-by-step solution to convert 160 minutes to hours:
Step 1: Write down the time conversion factor.
Step 2: Set up the conversion so that the unit you want to convert from (minutes) will be canceled out. In this case, you want to convert minutes to hours, so you will divide the number of minutes by the conversion factor.
Step 3: Substitute the given number of minutes into the equation.
Step 4: Perform the division.
Step 5: Interpret the result. Since the division does not result in a whole number, you have a decimal. The whole number part is the number of complete hours, and the decimal part represents the fraction of an hour.
In this case, 160 minutes is equal to 2 hours and approximately 0.6667 of an hour. To express this in minutes, you can multiply the decimal part by 60.
So, 160 minutes is equivalent to 2 hours and 40 minutes.
Final Answer: 160 minutes is equal to 2 hours and 40 minutes.
Step 1: Write down the time conversion factor.
Step 2: Set up the conversion so that the unit you want to convert from (minutes) will be canceled out. In this case, you want to convert minutes to hours, so you will divide the number of minutes by the conversion factor.
Step 3: Substitute the given number of minutes into the equation.
Step 4: Perform the division.
Step 5: Interpret the result. Since the division does not result in a whole number, you have a decimal. The whole number part is the number of complete hours, and the decimal part represents the fraction of an hour.
In this case, 160 minutes is equal to 2 hours and approximately 0.6667 of an hour. To express this in minutes, you can multiply the decimal part by 60.
So, 160 minutes is equivalent to 2 hours and 40 minutes.
Final Answer: 160 minutes is equal to 2 hours and 40 minutes.
Exercise 8 - Time pumps fill the reservoir
Exercise 9 - Tom and Becky paint a fence
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Exercise 8 - Time pumps fill the reservoir
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We have here a word problem, let's read it.
A water pump can fill a reservoir or a pool in 8 hours and there's another water pump,
and working on its own it would fill the same reservoir in 13 hours,
so the second pump is less efficient.
Now the question is, how long would it take for both pumps working
together simultaneously to fill that reservoir?
Obviously, it's not going to be 8 plus 13 which is 21,
it's going to be less than each of them,
going to be less than 8 hours because they're working together.
It's only going to reduce the time.
Now there's a standard approach for this problem is to introduce the concept of
a job that the whole filling the reservoir is 1 job.
Then we talk about the rates of each pump.
The rate of pump,
this one is called pump A and this is pump B so the rate of A,
if it does the whole job in 8 hours,
it's 1/8 of the job per hour and
the rate of B is 1/13 of a job per hour.
If you have difficulty with the concept of a job,
you could actually invent a number of gallons that you want.
You could say let the reservoir be 1,000 gallons and then do
1,000 over 8 gallons per hour and 1,000 over 13 gallons per hour.
The 1,000 is actually cancels out so you could use any number.
If you don't like the concept of the job,
then you could convert it to another unit or you could work in percentages,
say that the whole job is 100 percent and so on.
But I think you can understand the concept of the whole task is 1 job.
Now, what we do when the both working together is we add the rates.
We say that the combined rate or the simultaneous or together rate,
combined rate means both pumps working together we add the rate.
This does 1/8 of a job per hour,
and this does 1/13 of a job per hour together when they're working simultaneously,
they do 1/8 plus 1/13 jobs per hour, so to speak.
Now, in all these questions with jobs and rates,
it's always just like with distance that we have a standard formula that the work done,
let's say the portion of the job that each one does is
the rate in jobs per hour or whatever it is,
times the time multiplied by,
let me emphasize it and write the multiplication this way.
This has to be if it is in hours,
this is in jobs per hour.
If this is in seconds, this is in jobs per second and so on.
What we do is we do this for
the combined rate and we say the combined rate multiplied by the time,
the time that they were combined is equal to
portion of the job would be the whole job is 1.
What I'm saying is that the whole thing is 1 job equals the rate,
which is 1/8 plus 1/13
multiplied by the time we haven't assigned the variable yet but that time I'll call it
t. That's the how long is in t and I'm measuring it
in hours cause that's the unit I have chosen
for the rate also that's the only unit that is mentioned here,
so times t. Now that's a pretty straightforward equation because I now get that t is
equal to 1 over 1/8 plus 1/13 and push you could do this as a decimal on the calculator,
but let's practice fractions.
No. Let's just continue developing it.
Let's do the denominator first,
1/8 plus 1/13,
we put a common denominator and let it be 8 times
13 that's the least common denominator cause they have nothing in common so 8 times 13.
Well, I'll just write it as 8 times 13 and multiply it afterwards,
so,8 goes into 8 times 13,
13 times, so this is 13 over 13 times 8.
Here I multiply by 8,
so it's 8 over 8 times 13.
Basically, what is often done is if you choose the product to be the common denominator,
it's this diagonal plus this diagonal,
13 plus 8 over this.
Now remember when we take the reciprocal of a fraction,
we just invert the fraction so I can write it as 8 times 13 over 13 plus 8.
Now time to actually do some calculations.
I think we can do these in our head.
Certainly the 13 plus 8 is 21 is easy enough and let's see, 8 times 13.
Well, another 4 times 13 is 52 from playing cards or anyway.
8 times 13 is going to be double, 52 is 104,
or use the calculator or use multiplication pencil and paper.
This is what we get.
Then we do need a calculator for the final answer and this comes out.
My calculator says 4.952,
then rounding off to 4 places, this is what I make it.
That's approximately, of course and that is hours.
This is fine as the solution,
but I want to continue because sometimes they say,
oh, find the answer in hours and minutes maybe.
If it was in hours and minutes and this is the optional part,
so I'll use another color, what I would do,
I would say 4 hours and lets see,
how many minutes and something minutes.
Now how do I get the minutes?
I can just take this part here and multiply this by 60 minutes and if I do that,
then we get to the nearest minute, 57 minutes.
Again, this is approximately and I also say this is optional.
I'm just doing it cause sometimes they ask in hours and minutes,
so though usually not.
That's it. 4.95-4 hours and we're done.
This video explains how to solve a word problem involving two water pumps. The pumps are used to fill a reservoir or a pool, with the first pump taking 8 hours and the second pump taking 13 hours to fill the reservoir. The question is, how long would it take for both pumps working together simultaneously to fill the reservoir? The answer is 4.95 hours.
The solution involves introducing the concept of a job, with the whole filling the reservoir being 1 job. The rate of each pump is then calculated, with pump A doing 1/8 of a job per hour and pump B doing 1/13 of a job per hour. The combined rate is then calculated by adding the rates of the two pumps. The standard formula for work done is then used, with the combined rate multiplied by the time taken to fill the reservoir being equal to the whole job. The time taken is then calculated by dividing 1 by the combined rate. The answer is 4.95 hours, which can be converted to 4 hours and 57 minutes if required.
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