SOLUTION: Trying to help daughter with this problem and am at wits end.I guess I need a refresher algebra course if I'm going to survive this year. On a family trip, your father started o

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Question 24123: Trying to help daughter with this problem and am at wits end.I guess I need a refresher algebra course if I'm going to survive this year.
On a family trip, your father started out driving an average of 55 mph for 4 hours.Your mother, who was getting impatient, decided she would drive the rest of the way.She drove an aveage of 60 mph.How many hours did your mother drive? How many hours was the total trip if the average speed between both drivers was 58 mph. Any help would be appreciated!!
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
For this problem, you'll need to apply the concept of weighted averages.
Let x = the number of hours driven by mother. We can find the weighted average of father's speed plus mother's speed as follows:
The weighted average speed is given as: 58 mph.
58 mph = (father's distance + mother's distance)/total trip time.
Father's distance is: 55 mph(4 hrs)
Mother's distance is: 60 mph(x hrs)
The total trip time is (father's driving time) 4 hours plus (mother's driving time) x hours or (4+x) hours. Now you can write the equation for the weighted average speed for the trip which is given as 58 mph.
Simplify and solve for x. Multiply both sides by (4+x)
Simplify.
Subtract 58x from both sides.
Subtract 220 from both sides.
Divide both sides by 2.

So, mother's driving time is 6 hours.
Father's diving time is 4 hhours.
The total trip time is 6 hrs + 4 hrs = 10 hours.
Check:
Father's distance is 55 mph(4 hours) = 220 miles.
Mother's distance is 60 mph(6 hours) = 360 miles.
Total distance is 220 miles + 360 miles = 580 miles.
Total distance driven = weighted average speed (58 mph) X total driving time (10 hours).
Total distance driven = 58 mph X 10 hours = 580 miles.