Question

Brenda and her family were driving to her grandmother’s house during a holiday. During the drive, Brenda fell asleep halfway through the trip. When she awoke, her family still had to travel half the distance that she had

Answer 1

Let the whole trip = 1. She fell asleep at halfway = 1/2. When she awoke she had travelled x and the remaining distance = 1 − x. The clue says the remaining distance equals half the distance she had travelled: 1 − x = (1/2)x.

Solve: x + (1/2)x = 1 → (3/2)x = 1 → x = 2/3.

So she woke after travelling 2/3 of the trip. She fell asleep at 1/2, so she slept through 2/3 − 1/2 = 1/6 of the trip (≈16.67%).