# 2 families that live 270mi apart plan to meet for an afternoon picnic at a park that is located between their 2 homes. both families leave at 9:00 AM but one family averages 12mph faster then the other family. if the families meet at the designated spot 2.5 hr later, determine a. the average rate of speed for each family. b. the distance each family traveled to the picnic area.

1
by hazmine

2015-09-20T19:11:17+08:00

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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