It takes Maggie 20 min to drive to work in the morning. She drives home using the same route, but it takes 13 min longer, and she averages 8 mi/h less than in the morning. How far does Maggie drive to work?
Important information: the distance is the same each way
rate in the morning --- x mph
rate going home ----- x - 8 mph
D = R x T
in the morning : D = (20/60)x
going home : D = (33/60)(x-8)
(20/60)x = (33/60)(x-8) , multiply both sides by 60
20x = 33x - 264
13x = 264
x = 264/13 mph
so her distance = D = (20/60)(264/13) = 88/13 miles
or appr 6.77 miles
To find out how far Maggie drives to work, we need to first find her average speed in the morning. We know that it takes her 20 minutes to drive to work.
Using the formula speed = distance / time, we can rearrange it to find the distance:
distance = speed * time
Let's assume her average speed in the morning is S miles per hour. We need to convert the time from minutes to hours, so 20 minutes is equivalent to 20/60 = 1/3 hours.
Therefore, in the morning, the distance Maggie drives is: distance_morning = S * 1/3
Now, we know that in the evening it takes her 13 minutes longer to drive home. Therefore, her total driving time on the return journey is 20 + 13 = 33 minutes.
Converting 33 minutes to hours gives us 33/60 = 11/20 hours.
Her average speed in the evening is 8 mph less than in the morning, so her speed in the evening is S - 8 mph.
Hence, the distance Maggie drives on her return journey is: distance_evening = (S - 8) * 11/20
Since the distance to work in the morning is the same as the return journey in the evening, we can set up the equation:
S * 1/3 = (S - 8) * 11/20
To solve for S, we can cross multiply the equation:
20S = 11(S - 8)
20S = 11S - 88
Subtracting 11S from both sides gives us:
9S = -88
Dividing both sides by 9:
S = -88/9
However, a negative speed does not make sense in this context. This indicates an error in the problem or data provided.
Please double-check the information given or provide additional details to resolve the issue.