Mary left home at 12 noon and drove to visit her mom who liv

Mary left home at 12 noon and drove to visit her mom who lives 20 miles away. After she arrived she stayed for 2 hours. Afterwards she drove to her friend Sue\'s house who lives 15 miles from her mom. She arrived at Sue\'s at 3 oclock. If her speed heading for Sue\'s was 5 miles per hour faster than her speed going to her mom\'s, find her average speed on her way to Sue\'s.

Solution

Assume her speed on her way to Sue\'s was x miles/hr,so
her speed on her way to her mother\'s home was x-5 miles/hr .
By the given conditions, we see that
20/(x-5) + 2 + 15/x = 3 (2 and 3 means hours)
Cancel the denominators:
20x + 15(x-5) = x(x-5),
Simplify: x^2 - 40x + 75 =0,
By quadratic fromula ,we get
x = 5(4+sqrt(13)) or 5(4-sqrt(13))