We let the rate of the first family be x+12 or Rate₁ and the rate of the second family be x or Rate₂.
A. The average rate of speed for each family
Distance = Rate₁ * Time + Rate₂ * Time
Distance = Time * (Rate₁ + Rate₂)
270 = 2.5 * [(x + 12) + x]
270 = 2.5 * [2x + 12]
270 = 5x + 30
240 = 5x
48 = x
The average speed of the 1st family is 60 mph and the second has an average speed of 48 mph.
B. The distance each family traveled
Distance₁ = Time * Rate₁ = 2.5 * 60 = 150 miles
Distance₂ = Time * Rate₂ = 2.5 * 48 = 120 miles
