Given that,
Julia completes a 20-mile bike ride in 1.2 hours.
The distance Julia covers is 20 miles and her time taken is 1.2 hours.
Therefore, Julia's speed = 
= 16.67 mph
Katie finishes the same 20-mile ride in 1.6 hours.
Katie’s distance is 20 miles and her time is 1.6 hours.
Hence, Katie's speed = 
= 12.5 mph
To determine how much faster Julia rides compared to Katie, subtract Katie’s speed from Julia’s speed.
Thus, 16.67 mph minus 12.5 mph equals 4.17 mph, approximately 4.2 mph.
Consequently, Julia cycles 4.2 mph faster than Katie.
To determine the rates at which the inlet and outlet pipes fill and empty the reservoir, we remember that work done equals rate multiplied by time. Let’s denote the inlet rate as i and for the outlet pipe as 0. Therefore,
i(24) = 1
o(28) = 1
In this context, the '1' represents the total number of reservoirs, since the problem states the time needed for each pipe to either fill or empty a singular reservoir. Solving for rates yields:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour
Over the first six hours, the inlet pipe fills (1/24)(6) = 1/4 reservoirs and during the same period, the outlet pipe empties (1/28)(6) = 3/14 reservoirs. To calculate the net volume of the reservoir filled, we subtract the emptying total from the filling total:
1/4 - 3/14 = 1/28 reservoirs (note that if emptying exceeds filling, a negative value results. In such cases, treat that negative value as zero, indicating that the outlet rate surpasses the inlet rate, leading to an empty reservoir).
Now we need to find out how long it will take to fill up one reservoir since we’ve already partially filled 1/28 of it, after closing the outlet pipe. In simpler terms, we need to determine the time required for the inlet pipe to finish filling the remaining 27/28 of the reservoir. Fortunately, we have already established the filling rate for the inlet pipe, leading to the equation:
(1/24)t = 27/28
Solving for t gives us 23.14 hours. Remember to add the initial 6 hours to this result since the question seeks the total time. Thus, the final total is 29.14 hours.
Please ask me any questions you may have!
The domain refers to all potential input values, specifically represented by the x-axis on a graph. Conversely, the range includes all possible output values, depicted along the y-axis.
The graph clearly extends horizontally from (-∞,∞) on the x-axis, indicating that its domain is (-∞,∞).
Similarly, it can be seen that the graph stretches vertically from (-∞,∞) on the y-axis, denoting that the range is also (-∞,∞).
This indicates the function includes an infinite array of values. Therefore, there are no limitations on either the domain or the range for this function.
Answer:
Step-by-step explanation:
34+23F=175
23F=175-34=141
F=141/23≈6.13
therefore, he will purchase an additional 7 bags
Answer: He will require 10.07 cubic feet of sand for the wheelbarrows.
Step-by-step explanation:
Given that
the ratio of wheelbarrows filled with sand to those filled with concrete is expressed as
The volume of concrete in wheelbarrows is 248 cubic feet.
Then the volume of sand in wheelbarrows can be found as
Therefore, he will require 10.07 cubic feet of sand for the wheelbarrows.
