SOLUTION: 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 1

Question 2588: 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.
Found 2 solutions by khwang, kiru_khandelwal:
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
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))
Both positive, so there are two possible answer.

Answer by kiru_khandelwal(79) (Show Source): You can put this solution on YOUR website!
Let the speed with which mary goes to her mom place be x
So the speed with which mary goes to her freinds place will be x+5
Mary starts from her home at 12 noon and finally reaches her freinds place at 3'o clock....so total time take by mary is 3 hrs. This 3 hrs also include the time which mary stayed at her mom's place...which is 2 hrs
Now we know that
Time = distance/speed
so time taken by mary to gor from her house to her mom's house will be 20/x
time taken to go from mom's house to friends house will be 15/(x+5)
so total time taken is
20/x + 2 + 15/(x+5)
But total time taken is 3 hrs
so the equation will be
20/x + 2 + 15/(x+5) = 3
=> 20/x + 15/(x+5) = 1
=> (20x + 100 + 15x)/x(x+5) = 1
=> 35x + 100 = x(x+5)
=> 35x + 100 = x^2 + 5x
=> x^2 + 5x - 35x -100 = 0
=> x^2 -30x - 100 = 0
=> x = 15 +/-5*sqrt(13)
=> So the speed x will be 15 + 5*sqrt(13). It cant be the other one because speed cannot be negative.
So her speed to her mom's house is 15 + 5*sqrt(13)
and speed to sue's house will be 15 + 5*sqrt(13) + 5 = 20 + 5*sqrt(13)
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