Traveling in the direction of Hogwarts at a constant speed for the entire trip, Larry was one-eighth of the way to Hogwarts at 5:00 a. m. At 8:00 a. m. on the same day he was three-fourths of the way to Hogwarts. Knowing Larry's starting location and Hogwarts are in the same time zone, what time did Larry arrive at Hogwarts?

9:48 am

Step-by-step explanation:

In this question, we want to figure out the exact time Larry got to Hogwarts given the information in the question.

At 5.00am, he was 1/8 into the journey

At 8.00am he was 3/4 into the journey

The difference between these times is just 3 hours

what we need to do now is to calculate the fraction of the journey he had completed within the 3 hours

That would be 3/4 - 1/8 = 6-1/8 = 5/8

This means what is left of the journey to complete is simply 3/8 (1-5/8)

Now let’s have a representation;

5/8 completed within 3 hours

3/8 will be completed in x hours

To get c, we have x = (3/8 * 3)/5/8

(0.375 * 3)/0.625 = 1.8 hours

mathematically 1.8 hours is same as 1 hr 48 minutes

Let’s add this to 8am , this means he will get to hogwarts by 9;48 am

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.