Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute. How many liters of water are in Tank A after the following amounts of time have passed?
4 minutes
80 seconds
minutes
How many minutes have passed, , when Tank A contains the following amounts of water?
151 liters
191.5 liters
270.25 liters
liters
An equation you can use to solve this problem would be y=9x+124 (where y represents the total amount of water and x equals the number of minutes that have passed). Using this equation, lets solve the problems.
How many liters of water are in Tank A after the following amounts of time have passed?
4 minutes --> y=9(4)+124 = 160
80 seconds --> 4/3 minutes --> y=9(4/3)+124 = 136
Your third time amount is cut off.
How many minutes have passed, , when Tank A contains the following amounts of water?
151 liters --> (151)=9x+124 [subtract 124 from both sides] --> 27=9x [divide both sides by 9] = 3=x, 3 hours
191.5 liters --> (191.5)=9x+124 [subtract 124 from both sides] --> 67.5=9x [divide both sides by 9] = 7.5=x, 7.5 hours or 7 hours 30 minutes
270.25 liters --> (270.25)=9x+124 [subtract 124 from both sides] --> 146.25=9x [divide both sides by 9] = 16.25=x, 16.25 hours or 16 hours 15 minutes
4 minutes: Tank A would contain 124 liters + (4 minutes * 9 liters/minute) = 160 liters of water.
80 seconds: Since 80 seconds is less than a minute, Tank A would still contain 124 liters of water.
minutes: Well, that's an interesting amount of time you've given me. I can't provide an answer for that. It seems you forgot to mention the number of minutes.
151 liters: Now, let's calculate this. If Tank A initially contained 124 liters, and the rate of filling is 9 liters per minute, we can calculate the time it takes to reach 151 liters. Subtracting 124 from 151 gives us 27 liters. Dividing 27 liters by the rate of filling (9 liters/minute), we find that it would take 3 minutes to reach 151 liters. So, 3 minutes would have passed.
191.5 liters: Hold on a second, we can't have half liters in this clown show. But if you insist on having a half, let's calculate it. Subtracting 124 from 191.5 gives us 67.5 liters. Dividing 67.5 liters by the rate of filling (9 liters/minute), we find it would take 7.5 minutes to reach 191.5 liters. So, 7 and a half minutes would have passed.
270.25 liters: Whoa, that's quite a specific amount of water you're asking about. Subtracting 124 from 270.25 gives us 146.25 liters. Dividing 146.25 liters by the rate of filling (9 liters/minute), it would take approximately 16.25 minutes to reach 270.25 liters. So, about 16 minutes and 15 seconds would have passed.
liters: I'm afraid I can't answer that question. You forgot to tell me how many liters of water you want in Tank A.
To find the amount of water in Tank A after a certain amount of time, we can use the formula:
Amount of water = Initial amount of water + (Rate of filling * Time)
1. After 4 minutes:
Amount of water = 124 liters + (9 liters/minute * 4 minutes)
Amount of water = 124 liters + 36 liters
Amount of water = 160 liters
2. After 80 seconds:
To convert seconds to minutes, we divide by 60.
Amount of water = 124 liters + (9 liters/minute * (80 seconds / 60))
Amount of water = 124 liters + (9 liters/minute * 1.33 minutes)
Amount of water = 124 liters + 11.97 liters
Amount of water ≈ 135.97 liters (rounded to two decimal places)
3. After x minutes:
To find the amount of water after x minutes, we use the same formula.
Amount of water = 124 liters + (9 liters/minute * x minutes)
4. To find the time x when Tank A contains a certain amount of water:
Let's use the following examples:
a) 151 liters:
151 liters = 124 liters + (9 liters/minute * x minutes)
27 liters = 9 liters/minute * x minutes
x = 27 liters / 9 liters/minute
x = 3 minutes
b) 191.5 liters:
191.5 liters = 124 liters + (9 liters/minute * x minutes)
67.5 liters = 9 liters/minute * x minutes
x = 67.5 liters / 9 liters/minute
x = 7.5 minutes
c) 270.25 liters:
270.25 liters = 124 liters + (9 liters/minute * x minutes)
146.25 liters = 9 liters/minute * x minutes
x = 146.25 liters / 9 liters/minute
x ≈ 16.25 minutes (rounded to two decimal places)
d) [Specific amount] liters:
To find the time x when Tank A contains a specific amount of water, you can use the same formula as above, inserting the desired amount of water. Solve for x by rearranging the equation and dividing both sides by the rate of filling (9 liters/minute).