Let's denote the distance between Latoya's home and the mountains as D (in miles), the speed on the way there as S (in miles per hour), and the speed on the way back as S+27 (since it was 27 miles per hour faster).

From the problem, we know two things:

1. The time it took to get to the mountains (7 hours) is equal to the distance divided by the speed. So, we can write this as: D = 7S.

2. The time it took to get back home (4 hours) is also equal to the distance divided by the speed. However, the speed on the way back was faster (S+27). So, we can write this as: D = 4(S+27).

Since both equations are equal to D, we can set them equal to each other and solve for S:

7S = 4(S+27)

Expanding the right side gives: 7S = 4S + 108

Subtracting 4S from both sides gives: 3S = 108

Dividing both sides by 3 gives: S = 36 miles per hour.

Substitute S = 36 into the first equation to find D: D = 7S = 7*36 = 252 miles.

So, Latoya lives 252 miles away from the mountains.

Question

Let's denote the distance between Latoya's home and the mountains as D (in miles), the speed on the way there as S (in miles per hour), and the speed on the way back as S+27 (since it was 27 miles per hour faster).

From the problem, we know two things:

1. The time it took to get to the mountains (7 hours) is equal to the distance divided by the speed. So, we can write this as: D = 7S.

2. The time it took to get back home (4 hours) is also equal to the distance divided by the speed. However, the speed on the way back was faster (S+27). So, we can write this as: D = 4(S+27).

Since both equations are equal to D, we can set them equal to each other and solve for S:

7S = 4(S+27)

Expanding the right side gives: 7S = 4S + 108

Subtracting 4S from both sides gives: 3S = 108

Dividing both sides by 3 gives: S = 36 miles per hour.

Substitute S = 36 into the first equation to find D: D = 7S = 7*36 = 252 miles.

So, Latoya lives 252 miles away from the mountains.

Knowee AI · Accepted Answer