Luke rides his bike to his aunt's house. He travels 10 mi/h. Because it starts to rain, Luke's aunt drives him home in a car traveling at 25 mi/h. It takes Luke 1.5 h longer to get to his aunt's house than to return home. How many hours did it take Luke to ride to his aunt's house?

2.5 hours

Step-by-step explanation:

Let t = time in hours for reach friend's house

(t-1.5) = time for friend to drive her home

:

Both trips are the same distance, Write a distance equation from this fact:

Distance = speed * time

Drive distance = Bike distance

Equation-

step1)   25 (t-1.5) = 10t          (here u multiply 25 by t and 25 by 1.5)

step2)  25t - 37.5 = 10t        (move 37.5)          

step3)  25t - 10t = +37.5      (subtract 25t from 10t)

step4)  15t = 37.5                 (divide 37.5 by 15)

step5)  t = 2.5                     (time it took Luke to reach his aunt's house)

We can prove this by doing a statement and reason (more or less). The first thing we need to do is a construction of segment OG which is parallel to BC and touches A. Since it forms a straight line, we can say that m<OAB + m<A + m<GAC is equal to 180° (because it is a straight line). But, by alternate interior angles theorem, we can say that m<B = m<OAB and m<C = m<GAC. Therefore, by transitivity, m<A + m<B + m<C = 180°. Since angles A, B, and C are the interior angles of triangle ABC, we proved that the sum of the interior angles of ABC is 180°.