write and solve an inequality. on a trip from virginia to florida, the sampson family wants to travel at least 420 miles in 8 hours. what must be their average rate of speed?
8x ≥ 420
8x/8 ≥ 420/8
x ≥ 52.5
They would need to travel greater than or equal to 52.5 mpg to meet their expectations.
rate = distance / time
= 420/8 = 52.5 mph
so any speed greater than that will give a distance greater than 420
so
rate ≥ 420/8 would do it.
To write the inequality for this situation, we will need to use the formula:
Average Speed = Total Distance / Total Time
Let's assign variables:
Average Speed = x (in miles per hour)
Total Distance = 420 miles
Total Time = 8 hours
The inequality that represents the situation is:
x ≥ 420/8
Simplifying the inequality:
x ≥ 52.5
Therefore, the average rate of speed for the Sampson family must be at least 52.5 miles per hour.
To solve this problem, we need to set up an inequality that represents the situation and then solve for the average rate of speed.
Let's start by defining the average rate of speed as "r" in miles per hour (mph).
The distance traveled, d, can be determined using the formula: distance = rate × time.
Given that the Sampson family wants to travel at least 420 miles in 8 hours, we have the inequality:
distance ≥ 420 miles
rate × time ≥ 420 miles
r × 8 ≥ 420 miles
Now, to solve for r, we need to isolate it on one side of the inequality. Divide both sides of the inequality by 8:
(r × 8)/8 ≥ (420 miles)/8
r ≥ 52.5 mph
Therefore, the average rate of speed that the Sampson family must maintain to travel at least 420 miles in 8 hours is 52.5 mph.