Jen rode her bike 1/5 of a mile to her friend's house. It took her 5 minutes to get there. What was Jen's speed?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.

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.

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