Answer:
The distance to Jackie's friend house is 15 miles
Explanation:
The given parameters are outlined as follows;
1) The speed with which Jackie's dad drove her to her friends house = 30 mph
2) The speed Jackie's fiend mom drove her back home on the same route = 25 mph
The time it takes Jackie's friend mom to drive her back home = 6 minutes + The time it took Jackie's dad drove her to her friends house
Let the time, in minutes, it took Jackie's dad drove her to her friends house = t
Therefore;
The time it takes Jackie's friend mom to drive her back home = 6 + t
We have that speed = Distance/Time
∴ For Jackie's friend mom, her speed of 25 mph = (The distance of Jackie's friend house)/(6 + t)
Which gives;
The distance of Jackie's friend house = 25 × (6 + t)
Similarly, for Jackie's dad, his speed of 25 mph = (The distance of Jackie's friend house)/t
Which gives;
The distance of Jackie's friend house = 30 × t
By substitution, we have;
The distance of Jackie's friend house = 25 × (6 + t) = 30 × t
By the distributive property, we have;
150 + 25·t = 30·t
150 = 30·t - 25·t = 5·t
150 = 5·t
t = 150/5 = 30 minutes
t = 30 = 0.5 Hours
Using the equation for the distance to Jackie's friend house derived with the speed of motion of Jackie's dad, we have
The distance to Jackie's friend house = 30 × t = 30 mi/h × 0.5 h = 15 mi
The distance to Jackie's friend house = 15 miles
Similarly, from the equation derived from the speed of motion of Jackie's friend mom, we have;
The distance to Jackie's friend house = 25 × (6 + t) = 25 × (6 + 30)
The distance to Jackie's friend house = 25 mph × 36 minutes
The distance to Jackie's friend house = 25 miles per hour × 0.6 hours = 15 miles
The distance to Jackie's friend house = 15 miles.