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

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Question 82909: 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 3:00pm. If her speed heading for Sue's was 5 mph faster than her speed going to her mom's, find her average speed on the way to Sue's
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The time spent driving plus the 2 hours at her mom's adds up to the
elapsed time of 3 hours (noon to 3 PM).
If s is the average speed to her mom's, then s+5 is the average speed
from her mom's to Sue's
20%2Fs+%2B+2+%2B+15%2F%28s%2B5%29+=+3
This is just t%5B1%5D+%2B+2+%2B+t%5B2%5D+=+3
20%2Fs+%2B+15%2F%28s%2B5%29+=+1
Multiply both sides by s%28s%2B5%29
20%28s%2B5%29+%2B+15s+=+s%28s%2B5%29
20s+%2B+100+%2B+15s+=+S%5E2+%2B+5s
s%5E2+-+30s+-+100+=+0
Use the formula
s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-30
c+=+-100
s+=+%28-%28-30%29+%2B-+sqrt%28+%28-30%29%5E2-4%2A1%2A%28-100%29+%29%29%2F%282%2A1%29+
s+=+%2830+%2B-+sqrt%28900+%2B+400+%29%29%2F+2+
s+=+%2830+%2B-+sqrt%281300+%29%29%2F+2+
s+=+%2830+%2B-+10%2Asqrt%2813+%29%29%2F+2+
s+=+15+%2B-+5%2Asqrt%2813%29
s+=+15+%2B+5%2A3.6055
s+=+15+%2B+18.0278 (note that the other answer is negative and
therefore makes no sense)
s+=+33.028
But the average speed going to Sue's is s+%2B+5
s+%2B+5+=+33.028+%2B+5
s+%2B+5+=+38.028 mph answer
check answer
20%2Fs+%2B+2+%2B+15%2F%28s%2B5%29+=+3
Is this true when s+=+33.028?
20%2F33.028+%2B+2+%2B+15%2F38.028+=+3
.6056+%2B+2+%2B+.3944+=+3
1+%2B+2+=+3
OK