Jackie's dad drives her to a friend's house at the speed 30 mph. The friend's mom drives her back using the same route at the speed 25 mph. If the way back takes 6 minutes longer how far away is the friend's house?

The distance to Jackie's friend house is 15 miles

Step-by-step 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.

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step-by-step explanation: