Question

From the time Amanda gets up until her bus leaves at 8 a.m. She uses one seventh of the time having a shower, then one sixth of the remaining time getting dressed, and then one quarter of the remaining time having breakfast, which she finishes at exactly 7:15 am. At what time does she get up?

Answer 1

Answer: 12:50 am

Explanation:

Let's say Amanda gets up at time t, in hours.

Given that Amanda spends one-seventh of her time showering, this means she spends (1/7)×t hours in the shower.

The remaining time she has is 6/7 of her original time, so the amount of time she spends getting dressed is (1/6)×(6/7)t = (1/7)t hours.

After getting dressed, Amanda has (6/7)t - (1/7)t = (5/7)t hours left. She then spends one-quarter of this time having breakfast, which means she spends (1/4)×(5/7)t = (5/28)t hours having breakfast.

We are also given that Amanda finishes breakfast at exactly 7:15 am, which is 15 minutes before her bus leaves at 8:00 am. This means she has (8:00 - 7:15) = 45 minutes left after finishing breakfast, or (3/4) hours.

So we can set up the equation:

(5/7)t + (5/28)t = (3/4)

Multiplying both sides by the least common denominator of 28:

20t + 5t = 21

Simplifying:

25t = 21

t = 0.84

Therefore, Amanda gets up at 12:50 am.