QuestionJanelle hikes a 33-mile trail with a distance ratio walked to left as $4:7$ . How many miles has she walked?

Studdy Solution

STEP 1

Assumptions1. The total distance of the trail is33 miles. . The ratio of the distance Janelle has walked to the distance she has left to walk is47.

STEP 2

The ratio47 means that for every4 units of distance Janelle has walked, there are7 units of distance left to walk. We can express the total distance of the trail as the sum of these two parts.
$Total\, distance = Distance\, walked + Distance\, left\, to\, walk$

STEP 3

We can express the total distance in terms of the ratio. The total distance is the sum of the parts of the ratio, which is +7 =11 parts.
$Total\, distance =11\, parts$

STEP 4

To find the length of each part in miles, we divide the total distance by the number of parts.
$Length\, of\, each\, part = Total\, distance / Number\, of\, parts$

STEP 5

Plug in the values for the total distance and the number of parts to calculate the length of each part.
$Length\, of\, each\, part =33\, miles /11\, parts$

STEP 6

Calculate the length of each part.
$Length\, of\, each\, part =33\, miles /11\, parts =3\, miles/part$

STEP 7

Now that we know the length of each part, we can find out how many miles Janelle has walked. She has walked4 parts of the total distance.
$Distance\, walked = Number\, of\, parts\, walked \\times Length\, of\, each\, part$

STEP 8

Plug in the values for the number of parts walked and the length of each part to calculate the distance walked.
$Distance\, walked =4\, parts \\times3\, miles/part$

STEP 9

Calculate the distance walked.
$Distance\, walked =4\, parts \\times3\, miles/part =12\, miles$ Janelle has walked12 miles from the starting point of the trail.

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