answer:Let's break down the information given: 1. Mike prints 600 pamphlets per hour for x hours, then slows down to printing a third of that speed (200 pamphlets per hour) for 2 more hours. 2. Leo works for a third as many hours as Mike did before his break, meaning Leo works x/3 hours. His speed is twice that of Mike's initial speed, so he prints 1200 pamphlets per hour. 3. Together, they print 9400 pamphlets. Now let's set up equations: - For Mike: 600x + 200*2 = Total Pamphlets Printed by Mike - For Leo: 1200 * (x/3) = Total Pamphlets Printed by Leo Adding these together will give us the total number of pamphlets printed, which should equal 9400. 600x + 400 + 400*(x/3) = 9400 Multiplying through by 3 to clear the fraction gives us: 1800x + 1200 + 400x = 28200 Combining terms: 2200x = 27000 Dividing both sides by 2200: x = 12.27 (which is not a reasonable answer since we cannot have a fraction of an hour) It seems like there might be a mistake in the problem since it doesn't yield a reasonable solution. Could you please recheck the details?,To solve this problem, we need to determine the value of x, which represents the number of consecutive hours that Mike printed at his full speed. Let's break down the information given: Mike's printing speed before the break: 600 pamphlets per hour Mike's printing speed after the break: 1/3 * 600 = 200 pamphlets per hour Leo's printing speed: 2 * 600 = 1200 pamphlets per hour Number of hours Mike printed before the break: x Number of hours Mike printed after the break: 2 Number of hours Leo printed: 1/3 * x Total number of pamphlets printed: 9400 We can set up the equation as follows: Number of pamphlets Mike printed before the break + Number of pamphlets Mike printed after the break + Number of pamphlets Leo printed = Total number of pamphlets printed 600x + 200 * 2 + 1200 * (1/3 * x) = 9400 Let's simplify and solve for x: 600x + 400 + 400x = 9400 1000x + 400 = 9400 To isolate x, we subtract 400 from both sides of the equation: 1000x + 400 - 400 = 9400 - 400 1000x = 9000 To solve for x, we divide both sides of the equation by 1000: x = 9000 / 1000 x = 9 The value of x is 9. 9 The answer is: 9,To solve this problem, first we need to determine the speed at which Leo printed the pamphlets, given that he worked for only a third of the time Mike worked before his break, and that he was twice as fast as Mike: Leo's speed = 2 * Mike's speed Mike works for x hours, and after his break, he prints for 2 more hours. So the total time spent printing is x + 2 hours. Leo, however, only works for 1/3 of that time, which is (1/3)*(x + 2) hours. Now, let's calculate the total amount of pamphlets Leo prints: Number of pamphlets Leo printed = Speed * Time = Leo's speed * (1/3)*(x + 2) = 2 * Mike's speed * (1/3)*(x + 2) = (2/3)*(x + 2) * Mike's speed Similarly, we can calculate the number of pamphlets Mike printed: Number of pamphlets Mike printed = Speed * Time = Mike's speed * x = (x/x + 2) * 9400 (from the given information) = (x/x + 2) * 9400/2 since Leo's and Mike's time are equal except for the break Now, we can use the fact that the sum of the pamphlets printed by Mike and Leo equals 9400: Leo's printed pamphlets + Mike's printed pamphlets = 9400 (2/3)*(x + 2) * Mike's speed + (x/x + 2) * 9400/2 = 9400 Since we know that Mike's speed is 600 pamphlets per hour, we can substitute it: (2/3)*(x + 2) * 600 + (x/x + 2) * 9400/2 = 9400 Now, we can simplify the equation and solve for x: 400*(x + 2) + 4700*(x/x + 2) - 4350*(x + 2) = 9400 400*x + 800 + 4700*x/(x + 2) - 4350*x - 8700 = 9400 400*x + 800 + 4700*x/(x + 2) = 4350*x + 8700 5100*x - (4700*x)/(x + 2) = 9500 Multiply each side by (x + 2) and simplify: 5100*x*(x + 2) - 4700*x = 9500*(x + 2) 5100*x^2 + 10200*x - 4700*x = 9500*x + 19000 5100*x^2 + 5500*x - 19000 = 0 We can now solve for x using a quadratic equation solver or by factoring and applying the quadratic formula to find: x ≈ 3.43 So, Mike works for approximately 3.43 hours before his break.

answer:First, let's determine how many minutes are in 2 hours. To do this, we convert 2 hours into minutes: 2 hours × 60 minutes per hour = 120 minutes Now we need to calculate the total number of drops being administered throughout the treatment. During the 120 minutes, the saline drip will administer: 120 minutes × 20 drops per minute = 2400 drops Next, we need to calculate the volume in milliliters that the 2400 drops represent, since every 100 drops equals 5 ml. To do this, we convert 2400 drops to 100-drop units by dividing by 100: 2400 drops ÷ 100 = 24 units of 100 drops Now, we can determine the volume in milliliters by multiplying the total number of units of 100 drops by the amount of liquid each unit represents (5 ml): 24 units × 5 ml per unit = 120 ml So, the total volume of treatment in milliliters that the patient will receive after the 2 hours have passed is 120 ml., First, let's calculate how many drops the patient will receive during the 2-hour treatment. We know that there are 60 minutes in an hour, so: Total minutes = 2 hours * 60 minutes/hour = 120 minutes Now, we can find the total number of drops by multiplying the number of drops per minute (20) by the total number of minutes: Total drops = Drops per minute * Total minutes = 20 drops/minute * 120 minutes = 2400 drops Since every 100 drops equal 5 ml of liquid, we can convert the total number of drops into milliliters by dividing the total drops by 100 and then multiplying by 5: Volume (ml) = (Total drops / 100) * 5 = (2400 drops / 100) * 5 = 24 * 5 = 120 ml So, the patient will receive a total volume of 120 ml of treatment after the 2 hours have passed.,There are 60 minutes in 1 hour, so the treatment lasts for 2 hours x 60 minutes = 120 minutes. The saline drip administers 20 drops per minute, so in 120 minutes, the patient will receive 20 drops/minute x 120 minutes = 2400 drops. Every 100 drops equal 5 ml of liquid, so the patient will receive 2400 drops / 100 drops = 24 sets of 100 drops. Therefore, the patient will receive 24 sets x 5 ml = 120 ml of liquid. 120 The answer is: 120

answer:We don't have enough information to determine the value of x in this case. Please provide the time required to paint a house in hours instead of minutes., If it takes x minutes to paint a house and you want to find out how many houses can be painted in 3 hours, we first need to convert the time into minutes since x is given in minutes. We know that: 1 hour = 60 minutes So, 3 hours = 3 * 60 = 180 minutes Now, let's denote y as the number of houses that can be painted in 180 minutes. We can set up a proportion: x minutes (1 house) / 180 minutes (y houses) = 1 house / y houses Cross-multiplying, we get: x * y = 180 Since we're told that y = 9, we can substitute this value back into the equation: x * 9 = 180 x = 180 / 9 x = 20 So, if it takes x minutes to paint a house, and it is possible to paint 9 houses in 3 hours, then the value of x is 20 minutes.,We know that there are 60 minutes in an hour, so 3 hours is equal to 3 * 60 = 180 minutes. If it takes x minutes to paint a house, then in 180 minutes, you can paint 180/x houses. We are given that the number of houses you can paint in 3 hours is 9, so we can write: 180/x = 9. Solving for x, we get: x = 20. The value of x is 20. 20 The answer is: 20

answer:Let's denote the population of Lazy Harbor as y. According to the problem, the population of Port Perry is seven times that of Wellington, so it's 7x, and the population of Port Perry is 800 more than that of Lazy Harbor, so y = 7x - 800. We're asked to find the combined population of Port Perry and Lazy Harbor, which is 7x + y. However, we're given that this sum is equal to 11800. Since y = 7x - 800, we can substitute this into the equation to get: 7x + (7x - 800) = 11800 Now, we can solve for x: 14x - 800 = 11800 14x = 12600 x = 900 So, the population of Wellington is 900, and the population of Port Perry is 7 * 900 = 6300. The population of Lazy Harbor is 7 * 900 - 800 = 5500. Therefore, the population of Port Perry and Lazy Harbor combined is 6300 + 5500 = 11800.,We know that the population of Port Perry is seven times as many as the population of Wellington, which means the population of Port Perry is 7x. We also know that the population of Port Perry is 800 more than the population of Lazy Harbor, which means the population of Lazy Harbor is 7x - 800. The total population of Port Perry and Lazy Harbor combined is the sum of their populations: 7x + (7x - 800) = 14x - 800. We are given that the total population is 11800, so we can write: 14x - 800 = 11800. Adding 800 to both sides, we get: 14x = 12600. Dividing both sides by 14, we get: x = 900. The value of x is 900. 900 The answer is: 900,We are given the following information: 1. The population of Port Perry is seven times the population of Wellington. 2. The population of Port Perry is 800 more than the population of Lazy Harbor. 3. The total population of Port Perry and Lazy Harbor combined is 11,800. Let's use the variables W = population of Wellington, P = population of Port Perry, and L = population of Lazy Harbor. 1. We know that the population of Port Perry is seven times the population of Wellington: P = 7W 2. We know that the population of Port Perry is 800 more than the population of Lazy Harbor: P = L + 800 3. The total population of Port Perry and Lazy Harbor combined is 11,800: P + L = 11800 Now, we can substitute 7W for P and L + 800 for P in equation 3: 7W + L = 11800 (L + 800) + L = 11800 Combine like terms: 2L + 800 = 11800 Now, subtract 800 from both sides: 2L = 11000 Finally, divide both sides by 2: L = 5500 To find the population of Lazy Harbor, substitute 5500 for L in the equation L + 800 = P: 5500 + 800 = 6300 To find the population of Port Perry, substitute 6300 for L in the equation 7W = P: 7W = 6300 Divide both sides by 7: W = 900 So, the value of the unknown variable x, which represents the population of Wellington, is 900.