There are two roads that connect Emily's house and John's house. Emily told john that she drove 3/4 of the total distance from her house to john's house on one day, but she did not tell him which road she took.
A. using the long road, the distance between Emily's house and john's house is 12 miles.
B. using the short road, the distance between Emily's house and john's house is 1/2 the distance of the long road.
Which correctly explains the distance driven by Emily
A. She drove at least 0.5 miles , but at most 12 miles
B. she drove at least 4.5 miles, but at most 9 miles
C. she drove at least 5 miles, but at most 9 miles
D. she drove at least 9 miles, but at most 18 miles
I'll be glad to check your answer.
is it A.
How could she drive 12 miles when she only drove 3/4 of the length of the long road?
And what is 3/4 of 6?
so B
Right.
To solve this problem, we need to find the range of distances that Emily could have driven. We know that she drove 3/4 of the total distance from her house to John's house, but we don't know which road she took.
Let's start by finding the total distance between Emily's house and John's house using the long road. According to option A, the distance is 12 miles.
Next, let's find the distance using the short road. According to option B, the distance using the short road is 1/2 of the distance of the long road. So, the distance using the short road would be (1/2) * 12 = 6 miles.
Now, we know that Emily drove 3/4 of the total distance, regardless of the road she took. So, if she drove 3/4 of 12 miles, she would have driven 3/4 * 12 = 9 miles if she took the long road.
Similarly, if she took the short road, she would have driven 3/4 of 6 miles, which is 3/4 * 6 = 4.5 miles.
Therefore, the correct range of distances that Emily could have driven is between 4.5 miles (if she took the short road) and 9 miles (if she took the long road). So, the correct answer is option B: she drove at least 4.5 miles, but at most 9 miles.