Answer:
See below
Step-by-step explanation:
a. Since they tell you the amount of water increases 1/4 gallon in 2/5 minutes, you can also see that you'd have 2/4 gallons in 4/5 minutes. Then 3/4 gallons in 6/5 minutes; 4/4 or 1 gallon in 8/5 minutes. Finally you can go one more step and see that you would have 5/4 gallons or 1 1/4 gallons in 10/5 minutes.
10/5 minutes is equal to 2 minutes. so if you divide the gallons by 2 you'll know how many gallons you'd have in 1 minute. 5/4 divided by 2 is equal to 5/8 gallons.
Another way you can look at this is if you have 1/4 gallon in 2/5 of a minute, then you would only have half of the 1/4 gallon in 1/5 of a minute. Half of 1/4 gallon is equal to 1/8 of a gallon. So if you are getting 1/8 gallon in 1/5 of a minute, you can multiply them both by 5 to get your answer in gallons/minute.
5 times 1/8 is 5/8 and 5 times 1/5 minutes is 5/5 minutes or 1 minute.
So you get the same answer 5/8 gallons/minute
b. Above you calculated how many gallons you will get in 1 minute. So to figure out how much you will get in 5 minutes, you'd multiply 5/8 by 5. This gives you 25/8 or 3 1/8 gallons. If you started with 6 gallons in the tub, now you just add those two numbers together to get 9 1/8 gallons.
c. Again we can look at the sink the same as the bath tub. Keep adding the gallons and minutes until you can get the minutes fraction equal to a whole number. 3/5 gallon in 4/5 minutes double to be 6/5 gallons in 8/5 minute, 9/5 gallons in 12/5 minutes, 12/5 gallons in 16/5 minutes and finally 15/5 gallons in 20/5 minutes. 20/5 minutes is the same as 4 minutes in whole numbers.
So if you divide both the gallons and minutes by 4, you'll get how many gallons you're getting in 1 minute. 15/5 gallons divided by 4 is 15/20 gallons. This can be reduced down to 3/4 gallons. When you divide 4 minutes by 4, you get 1 minute. So the sink is getting 3/4 gallon/minute.
Which is getting more water per minute? 3/4 gallons/minute is more than 5/8 gallons/minute so the sink is filling more rapidly.
