Answer:
hope it help
Step-by-step explanation:
you need to use the D(istance) = R(ate) * T(ime) equation. Here the distance is 12 miles both ways. Let x be the rate on her way home, then x + 15 is the rate on her way there. We know it took Jen 3 hours for the round trip.
We need to find the time it took Jen to go to her friend's house.
12 = (x + 15) * Tto friend's house
Solve for Tto friend's house.
Divide both sides by (x + 15):
12 / (x + 15) = Tto friend's house
We need to find the time it took Jen to return home from her friend's home.
12 = x * Tfrom friend's house
Solve for Tto friend's house.
Divide both sides by x:
12 / x = Tfrom friend's house
We know the round trip took 3 hours, therefore:
Tto friend's house + Tfrom friend's house = 3
Substitute for the two times:
12 / (x + 15) + 12 / x = 3
The common denominator is: x * (x + 15).
(12 * x + 12 * (x + 15)) / (x * (x + 15)) = 3
Multiply both sides by x * (x + 15):
12x + 12x + 180 = 3 * x * (x + 15)
24x + 180 = 3x2 + 45x
Subtract 24x from both sides:
180 = 3x2 + 21x
Subtract 180 from both sides and rearrange:
3x2 + 21x - 180 = 0
Divide all terms by 3:
x2 + 7x - 60 = 0
We need to find two factors when multiplied will equal -60 and when added will equal 7.
The factors are -5 and 12.
(x + 12) * (x -5 ) = 0
Use the zero product rule:
x + 12 = 0, x = -12.
x - 5 = 0, x = 5
Replace x in the two equations to find the time to Jen's friend's house and returning from Jen's friend's house.
To her friend's house:
12 / (x + 15) = Tto friend's house
12 / (5 + 15) = Tto friend's house
12 / 20 = .6, or the trip to Jen's friend's house took .6 hours or 36 minutes.
From her friend's house:
12 / x = Tfrom friend's house
12 / 5 = Tfrom friend's house
12 / 5 = 2.4, or the trip from Jen's friend's house took 2.4 hours or 2 hours and 24 minutes.
Using -12 in the 12 / x = Tfrom friend's house will result in negative time. This solution can be discarded.