This is not a question, but six problems with answers, so please review them. If I have any wrong then please explain how to do it step by the step for the answer and suggest any thing. Thank you tutors.
Solve.
1. Sasha can mow 3/8 of an acre of grass in 45 minutes. How many acres of grass does Sasha mow per hour?
My answer: Sasha can mow 1/2 acre of grass per hour.
2. Ammar hikes 2 3/4 miles of nature trail in 1 hour and 15 minutes. How many miles of trail does Ammar hike per hour?
My answer: Ammar can hike 2 1/5 miles of trail per hour.
3. Melinda paints 7/8 of a wall in 1 1/6 hours. what part of a wall does Melinda paint in 1 minute?
My answer: Malinda paints 3/4 part of a wall in 1 minute.
4. There is 1/4 ounce of yeast in every 2 1/4 teaspoons of yeast. A recipe for bread calls for 2 teaspoons of yeast. How many ounces of yeast are needed for this recipe?
My answer: 2/8 oz of yeast are needed for this recipe
5. Every 5 1/2 cups of flour weighs 1 9/16 pounds. Use a unit rate to show how you could determine if there are more than or less than 35 cups of flour in a 10-pound bag of flour.
My answer: Unit rate: 3 13/25 cups of flour per pound. Multiply by 10 to see the amount of cups in a 10-pound bag of flour.
6. One tank is filling at a rate of 5/8 gallon per 7/10 hour. A second tank is filling at a rate of 5/9 gallon per 2/3 hour. Which tank is filling faster? Explain how you know.
My answer: The first tank is filling faster. How I know this is because the unit rate for the first tank is 25/28 gallon per hour and the second is 5/6 gallon per hour and 25/28 as a decimal is .89 rounded while the second as a decimal is .83 rounded. The rates are being compared so they should be the same so I chose unit rate as the second quantity because both second quantities being compared need to be the same.
Thank you for sparing your time to review my work.
1. Sasha can mow 3/8 of an acre in 45 minutes. To find out how many acres Sasha can mow per hour, we need to determine how many sets of 45 minutes are in an hour. Since there are 60 minutes in an hour, we can set up a proportion:
45 minutes / 60 minutes = 3/8 acre / x acres
Cross-multiply:
45x = 60 * (3/8)
Simplify:
45x = 180/8
45x = 22.5
x = 22.5 / 45
x = 0.5 acres
Therefore, Sasha can mow 0.5 acres of grass per hour.
2. Ammar hikes 2 3/4 miles of nature trail in 1 hour and 15 minutes. To find out how many miles of trail Ammar hikes per hour, we need to determine how many sets of 1 hour and 15 minutes are in an hour. Since there are 60 minutes in an hour, we can convert 1 hour and 15 minutes to minutes:
1 hour = 60 minutes
1 hour and 15 minutes = 60 minutes + 15 minutes = 75 minutes
Now we can set up a proportion:
75 minutes / 60 minutes = 2 3/4 miles / x miles
Cross-multiply:
75x = 60 * (11/4)
Simplify:
75x = 660/4
75x = 165
x = 165 / 75
x = 2 1/5 miles
Therefore, Ammar hikes 2 1/5 miles of trail per hour.
3. Melinda paints 7/8 of a wall in 1 1/6 hours. To find out what part of a wall Melinda paints in 1 minute, we need to determine how many minutes are in 1 1/6 hours.
1 hour = 60 minutes
1 1/6 hours = 60 minutes + 10 minutes = 70 minutes
Now we can set up a proportion:
1 1/6 hours / 70 minutes = 7/8 wall / x wall
Cross-multiply:
(7/8) * 70 = x
Simplify:
x = 49/8
x = 6 1/8
Therefore, Melinda paints 6 1/8 parts of a wall in 1 minute.
4. There is 1/4 ounce of yeast in every 2 1/4 teaspoons of yeast. The recipe calls for 2 teaspoons of yeast. To find out how many ounces of yeast are needed for this recipe, we need to set up a proportion:
(1/4 ounce) / (2 1/4 teaspoons) = x ounces / 2 teaspoons
Cross-multiply:
(1/4) * 2 = (2 1/4) * x
Simplify:
1/2 = (9/4) * x
Now, divide both sides of the equation by 9/4:
1/2 ÷ (9/4) = x
1/2 * (4/9) = x
2/18 = x
1/9 = x
Therefore, 1/9 ounce of yeast is needed for this recipe.
5. Every 5 1/2 cups of flour weighs 1 9/16 pounds. To determine if there are more than or less than 35 cups of flour in a 10-pound bag, we can use unit rate to find how many cups of flour per pound:
(5 1/2 cups) / (1 9/16 pounds) = x cups / 1 pound
Cross-multiply:
(5 1/2) * 1 = (1 9/16) * x
Simplify:
11/2 = (17/16) * x
Now, divide both sides of the equation by 17/16:
11/2 ÷ (17/16) = x
11/2 * (16/17) = x
88/34 = x
44/17 ≈ x
The unit rate is approximately 44/17 cups of flour per pound. Now, to determine if there are more or less than 35 cups of flour in a 10-pound bag, we can multiply the unit rate by 10:
(44/17) * 10 = 8 14/17 cups
Therefore, there are more than 35 cups of flour in a 10-pound bag.
6. The first tank is filling at a rate of 5/8 gallon per 7/10 hour. The second tank is filling at a rate of 5/9 gallon per 2/3 hour. To determine which tank is filling faster, we need to compare the rates.
To compare the rates, we can find the unit rate for both tanks:
First Tank: (5/8 gallon) / (7/10 hour) = (5/8) * (10/7) = 50/56 = 25/28 gallon per hour
Second Tank: (5/9 gallon) / (2/3 hour) = (5/9) * (3/2) = 15/18 = 5/6 gallon per hour
Since the first tank has a unit rate of 25/28 gallon per hour and the second tank has a unit rate of 5/6 gallon per hour, the first tank is filling faster.
Therefore, the first tank is filling faster than the second tank.
3 and 4 are wrong
#3 probably contains a typo, and it must have asked for the rate per hour, not per minute
She did paint 3/4 of the wall in 1 HOUR.
#4, check your calculation, you are close.
You did multiply your quotient answer by 2 ??
For #3 it was asking for per minute, how do I find for per minute ?
#4 Yes, I got 1/9 for the quotient the multiplied by 2. I did that because it was asking for 2 teaspoons and I found the unit rate for only per teaspoon, so having the unit rate I multiplied it by 2. My quotient was 5/45 then I just simplified. I'm still getting 1/9 if I simplify 4/36. Is it just 1/9 ?
#4
but you typed 2/8, not 2/9
that is why both me and Bob labeled it incorrect.
yes, the correct answer is 2/9
#3
so we have 3/4 wall in 1 hour
or 3/4 wall in 60 minutes
thus (3/4)÷60 or 1/80 of a wall in 1 minute
For #4, sorry my bad, looks like I didn't double check my answer.
For #3, thank you very much for the explanation, I understand now. But, in my class just today, the way someone did it was by dividing by 70, I should've asked why. Either way the answer is still 1/80.
Thank you tutor Reiny and bobpursley for checking my work.