Question

Water flows through a pipe at a rate of 830 cups every 3.5 weeks. Express this rate of flow in liters per day. Round your answer to the nearest hundredth.

Answer 1

To convert the flow rate of 830 cups every 3.5 weeks to liters per day, you multiply the number of cups by 0.24 to convert to liters, find the number of days in 3.5 weeks, and divide the total liters by the number of days, resulting in approximately 8.13 liters per day.

Step-by-step explanation:

The student is asking to convert a flow rate of 830 cups every 3.5 weeks into liters per day. Since 1 cup is approximately 0.24 liters, we start by converting cups to liters:

• 830 cups × 0.24 liters/cup = 199.2 liters (every 3.5 weeks)

Next, we need to find out how many days are in 3.5 weeks to convert the flow rate into liters per day:

• 3.5 weeks × 7 days/week = 24.5 days

Now, we divide the total liters by the number of days:

• 199.2 liters / 24.5 days ≈ 8.13 liters/day

Therefore, the water flows at a rate of approximately 8.13 liters per day.

Answer 2

6.08 L/d

Step-by-step explanation:

The data is provided in units of cups (c) and weeks (w). If we divided 630 cups by 3.5 weeks, we would have a rate:

(630 cups)/(3.5 weeks) = 180 cups/week (c/w)

We are asked for a rate in liters per day, or L/d. Lets find a conversion factor to make that change.

We want to go from (c/w) to (L/d).

We know that:

1) There are 4.23 cups in a liter, or 4.23 c/L

2 There are 7 days in a week, or 7 d/w

We want to convert 180 (c/w) to L/d

180 (c/w)

Starting with just the unit:

(c/w)

The second conversion from above tells us that 7 d/w. The beauty of conversion factors is that they can be inverted. 7 d/w is the same as 1w/7d Lets write that as (1/7)w/d.

Now multiply times the original rate:

180 (c/w)*((1/7)(w/d)

The unit w (weeks) cancels, leaving cups, c and d (days): 25.71 c/d

Now use the second conversion factor to change cups, c, to Liters, L.

4.23 c/L [From above]

This can be done as a division with the original unit:

(25.71 c/d)/(4.23 c/L) = 6.08 L/d

c, cups, cancel and L. liters. moves to the top.

For those of us who prefer multiplication over division, it is easy to invert the conversion factor and then multiply, instead of divide:

The inverted factor is

(25.71 c/d)*(0.235 L/c) = 6.08 L/d

Cups, c, cancel, leaving L/d, the desired unit.