The question asks how much additional time in hours the cyclist needs to ride the remaining distance to reach 45 miles total after already riding 18 miles in 1.5 hours. The rate relationship is speed in miles per hour, which is distance divided by time. First, calculate the speed: 18 miles / 1.5 hours = 12 miles per hour, ensuring units are consistent as miles over hours. The remaining distance is 45 miles - 18 miles = 27 miles, so additional time = 27 miles / 12 miles per hour = 2.25 hours, with units canceling to hours. A common error is forgetting to subtract the initial distance and calculating time for the full 45 miles instead. Always verify units in rate problems to avoid mismatches, such as confusing hours with minutes.

The question asks how long the bus trip takes in hours to the nearest tenth, given 132 miles at 48 miles per hour. The rate relationship is time in hours as distance over speed. Calculate: 132 miles / 48 miles per hour = 2.75 hours, with miles canceling to hours. Round 2.75 to nearest tenth: 2.8 hours. A common error is rounding incorrectly, like to 2.7. Perform division precisely and apply rounding rules only at the end for accuracy.

The question asks how many more minutes are needed to finish a 1,260-word essay after typing for 12 minutes at 42 words per minute. The rate relationship is typing speed in words per minute. First, words already typed: 42 words/minute * 12 minutes = 504 words, units canceling to words. Remaining: 1,260 - 504 = 756 words, time = 756 / 42 = 18 minutes, words canceling to minutes. Errors include not subtracting typed words, calculating total time. Calculate completed work first in multi-step rate problems to find remaining accurately.

The question asks for the unit rate in dollars per notebook, represented by the slope of the cost line through (2,5) and (8,17). The rate relationship is cost per notebook as slope, change in cost over change in notebooks. Calculate slope: (17 - 5) dollars / (8 - 2) notebooks = 12 / 6 = 2 dollars per notebook, units dollars over notebooks. This gives the variable rate. Errors include using total cost instead of changes. Use the slope formula with deltas to find rates in coordinate graphs.

The question asks for the car's fuel efficiency in miles per gallon, given 270 miles on 9 gallons. The rate relationship is miles per gallon, distance divided by fuel used. Calculate: 270 miles / 9 gallons = 30 miles per gallon, with units miles over gallons directly. This assumes constant consumption. A common mistake is inverting to gallons per mile. Remember, efficiency is typically distance per unit fuel, so set up the fraction accordingly.

The question asks which plan has the lower unit rate in dollars per GB and what that rate is. The rate relationship is cost per GB for each plan, total cost over data. For Plan A: $18 / 6 GB = $3 per GB; Plan B: $25 / 10 GB = $2.5 per GB, units dollars over GB. Plan B is lower at $2.5/GB. A key error is comparing total costs without unit rates, missing the per-GB value. Compare rates by calculating each separately and ensuring units match for fair comparison.

The question asks how many hours it takes to assemble 50 devices, given 24 in 6 hours at a constant rate. The rate relationship is assembly rate in devices per hour, total devices over time. Calculate rate: 24 devices / 6 hours = 4 devices per hour, units devices over hours. Time for 50: 50 devices / 4 devices per hour = 12.5 hours, canceling devices to hours. A common mistake is proportional scaling without finding unit rate, like 6/24 * 50. Always find the unit rate first for straightforward multiplication or division.

The question asks how many hours it takes to drain 5,400 gallons at 15 gallons per minute, converting to hours. The rate relationship is drainage in gallons per minute, but we need time in hours. First, time in minutes: 5,400 gallons / 15 gallons per minute = 360 minutes, with gallons canceling to minutes. Convert to hours: 360 minutes / 60 minutes per hour = 6 hours, ensuring proper unit conversion. Errors include not converting minutes to hours or misplacing units in division. When rates are in minutes but answer in hours, calculate time first then convert units step-by-step.

The question asks how many minutes it takes for the train to travel 100 miles, given 240 miles in 3 hours, with conversion from hours to minutes. The rate relationship is speed in miles per hour, distance over time. Calculate speed: 240 miles / 3 hours = 80 miles per hour, units miles over hours. Time for 100 miles: 100 miles / 80 mph = 1.25 hours, then convert 1.25 hours * 60 minutes/hour = 75 minutes, ensuring unit conversion. A key error is forgetting to convert hours to minutes, leaving the answer in hours. Always check the required units and perform conversions after calculating in consistent base units.

The question asks how many cups of flour are needed for 20 muffins, scaling from 3.5 cups for 14 muffins proportionally. The rate relationship is flour per muffin, in cups per muffin, found by dividing total flour by number of muffins. Calculate the rate: 3.5 cups / 14 muffins = 0.25 cups per muffin, with units cups over muffins. For 20 muffins: 0.25 cups/muffin * 20 muffins = 5 cups, canceling muffins to leave cups. Errors often occur by not finding the unit rate first, like directly multiplying 3.5 by 20/14 without simplifying. Set up proportions carefully, ensuring consistent units on both sides.