Question - Calculating Miles Driven Over Time
Solution:
To solve this question, let's do it step by step.a) To find the unit rate, we determine the number of miles Meng can drive in one hour. The unit rate is found by dividing the total distance by the total time. The equation would be:Unit rate = Total miles / Total hoursPlug in the numbers:Unit rate = 150.75 miles / 4.5 hours = 33.5 miles/hourSo Meng drives at a rate of 33.5 miles per hour.b) The constant of proportionality, $$ k $$, in this context is the same as the unit rate since it represents the constant value that relates the number of hours driven to the number of miles covered. Therefore, $$ k = 33.5 $$ miles per hour.c) To complete the table, multiply the constant of proportionality, $$ k $$, by each number of hours.For 1 hour:Miles = k * Hours = 33.5 miles/hour * 1 hour = 33.5 milesFor 2 hours:Miles = k * Hours = 33.5 miles/hour * 2 hours = 67 milesFor 3 hours:Miles = k * Hours = 33.5 miles/hour * 3 hours = 100.5 milesFor 4 hours:Miles = k * Hours = 33.5 miles/hour * 4 hours = 134 milesFor 5 hours:Miles = k * Hours = 33.5 miles/hour * 5 hours = 167.5 milesTherefore, the completed table is:| Hours | 1 | 2 | 3 | 4 | 5 ||-------|-------|------|--------|-------|--------|| Miles | 33.5 | 67 | 100.5 | 134 | 167.5 |
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