# Algebra

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It is 74.4 miles from Dwane and Patti's house to Martha's house. Patti leaves home at 10:00 and drives toward Martha's house. Dwane and Martha set off half an hour later from their own houses and drive toward the other's house. The average speed of the three friends is 54 mph and they all meet at 11:06. How fast does each drive?

• Algebra -

This is quite confusing problem and the people setting the problem should keep common sense handy when designing a problem.

The confusion is created because Dwane and Patti live in the same house but leave at different times to go to meet the same person Martha at the same time and point on the road. More confusing is Martha also leaves her house same time as Dwane. Considering this is car driving (the distance is 74.4 miles) it doesn't make much sense and then all-three meet in-between. That it just not a close to real life situation.

In any case, the once this is understood the problem is simple: Speeds P(Patti)+D(Dwane)+M(Martha)=3x54, 1.1P=0.6D (As Patti and Dwane travel the same distance in 1.1 hr and 0.6 hr), and 0.6D+0.6M=74.4 (Dwane and Martha's distance added to the total distance).

Solving these three equations:
P+D+M=162
1.1P=0.6D
0.6D+0.6M=74.4

That gives:
P=38 mph
D=69 2/3 or 69.67 mph
and
M=54 1/3 or 54.33 mph