Question

3 question's for 60 points?                            

1.
At 12:00 p.m., Jane leaves her house and drives north to the beach.
She arrives at 1:30 p.m. Also leaving at 12:00 p.m., her brother Paul leaves her house and drives south to a state park. He arrives at 2:30 p.m. The driving distance from the beach to the state park is 240 mi. Jane and Paul drove at the same speed. What was their speed?

2.
Catie is 3 years older than her brother. The sum of their ages is no more than 31.
Write an inequality that can be used to represent this situation, where x represents Catie's brother's age. What is the oldest age Caties's brother can be?

3.
June's father is 6 times as old as June. The sum of their ages is no less than 77.
Find an inequality that can be used to represent this situation, where x represents Julio's age. What is the youngest age Julio can be in the second box?

Answer 1

1.) Let their speed be x, then distance travelled = speed x time
1.5x + 2.5x = 240
4x = 240
x = 240/4 = 60
Their speed is 60 miles per hour.

2.) Let catie's brother's age be x, then catie's age is 3 + x
x + 3 + x ≤ 31
Required inequality is 2x + 3 ≤ 31
2x ≤ 31 - 3
2x ≤ 28
x ≤ 28/2
x ≤ 14

Therefore, the oldest age Catie's brother can be is 14 years old.

3.) Let June's age be x, then her father's age is 6x
6x + x ≥ 77
7x ≥ 77
x ≥ 77/7
x ≥ 11

The youngest age Julio can be is 11 years old.