A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad picks her up and drives her through the remainder of the way at 30 miles per hour. If they arrived at school at 9:00, how far did she walk?
Let n be the distance she walks, and 20-n be the distance she rides. Then:
n/3+(20-n)/30=13/6
10n+20-n=65
9n=45
n=5
She walked 5 miles; and rode for 15
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To find out how far the girl walked, we need to calculate the distance she covered from 6:50 to the point her dad picked her up.
Let's first determine the duration of time she walked. We know that she arrived at school at 9:00, which means she walked for 2 hours and 10 minutes (9:00 - 6:50 = 2 hours and 10 minutes).
Next, we'll convert the time into minutes. Since there are 60 minutes in an hour, 2 hours is equal to 120 minutes. Adding 10 minutes gives us a total of 130 minutes.
Now, let's calculate the distance she covered on foot. Her walking speed is 3 miles per hour, which means she walks 3 miles in 1 hour. Therefore, she will walk 3 miles in 60 minutes.
Since she walked for 130 minutes, we can apply a proportion to find the distance she covered:
Distance walked / Time taken to walk = Walking speed
Distance walked / 130 minutes = 3 miles / 60 minutes
Cross-multiplying the equation, we get:
Distance walked = (3 miles / 60 minutes) * 130 minutes
Simplifying further:
Distance walked = (1/20) miles/minute * 130 minutes
Now, multiplying the fractions:
Distance walked = (1 * 130) / (20)
Distance walked = 130 / 20
Distance walked = 6.5 miles
Therefore, the girl walked a total distance of 6.5 miles.