Multiply & Divide Rational Numbers Quick Check
3 of 53 of 5 Items
Question
Solve this multi-step problem. A runner completes 14 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
18 mile
Start Fraction 1 over 8 End Fraction mile
160 miles
160 miles
110 mile
Start Fraction 1 over 10 End Fraction mile
212 miles
The correct answer is: "Start Fraction 1 over 8 End Fraction mile"
A water tank decreases by 10 gallons every 3 hours every day. What is the total change in the amount of water in the tank after 6 days?(1 point)
Responses
480 gallons
480 gallons
80 gallons
80 gallons
−80 gallons
negative 80 gallons
−480 gallons
To find the total change in the amount of water in the tank after 6 days, we need to find the change per day and then multiply it by the number of days.
The tank decreases by 10 gallons every 3 hours, so in one day (which is 24 hours), the tank will decrease by (10/3) * 8 gallons.
So, in 6 days, the tank will decrease by (10/3) * 8 * 6 gallons.
Calculating this, we get:
(10/3) * 8 * 6 = 160 gallons.
Therefore, the correct answer is: "160 gallons".
A recipe calls for 13 of a container of yogurt. Each container of yogurt has 150 calories. The recipe makes 4 servings. Which set of calculations would give the correct number of calories per serving?(1 point)
Responses
13×150÷14
Start Fraction 1 over 3 End Fraction times 150 divided by Start Fraction 1 over 4 End Fraction
13×150×4
Start Fraction 1 over 3 End Fraction times 150 times 4
13÷150÷4
Start Fraction 1 over 3 End Fraction divided by 150 divided by 4
13×150÷4
To find the correct number of calories per serving, we need to divide the total number of calories (13 containers of yogurt * 150 calories per container) by the number of servings (4 servings).
So, the set of calculations that would give the correct number of calories per serving is:
13 * 150 ÷ 4.
Calculating this, we get:
(13 * 150) ÷ 4 = 487.5 calories per serving.
Therefore, the correct answer is: "13 * 150 ÷ 4".
To solve this multi-step problem, we need to find out how far the runner can go in 16 minutes at the same pace.
First, we know that the runner completes 1/4 of a 5-mile race every 8 minutes. This means that the runner can go 5/4 miles in 8 minutes.
To find out how far the runner can go in 16 minutes, we can set up a proportion:
(5/4 miles) / (8 minutes) = x / 16 minutes
To solve this proportion and find the value of x, we can cross multiply:
8 * x = 16 * (5/4)
8x = 20
Then, we can solve for x by dividing both sides by 8:
x = 20/8
So, the runner can go 2.5 miles in 16 minutes. Therefore, the correct response is:
2.5 miles
To solve this multi-step problem, we need to calculate the distance the runner can go in 16 minutes at the same pace.
First, we need to find the distance the runner can cover in 1 minute. We know that the runner completes 1/4 of a 5-mile race every 8 minutes. So, we can divide 5 by 8 to find the distance the runner covers in 1 minute.
5 miles ÷ 8 minutes = 0.625 miles/minute
Therefore, the runner can cover 0.625 miles in 1 minute.
To find the distance the runner can go in 16 minutes, we multiply the distance covered in 1 minute by 16.
0.625 miles/minute × 16 minutes = 10 miles
Hence, the runner can go 10 miles in 16 minutes.
Therefore, the correct response is "10 miles."