SOLUTION: meslissa walks 3 miles to the house of a friend an returns home on a bike she averages 4 miles per hour faster when cycling than walking and the total time for both trips is two ho

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Question 1049953: meslissa walks 3 miles to the house of a friend an returns home on a bike she averages 4 miles per hour faster when cycling than walking and the total time for both trips is two hours find her walking speed
Found 2 solutions by josmiceli, advanced_Learner:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed walking
+s+%2B+4+ = her speed biking
Let +t+ = her time walking
+2+-+t+ = her time biking
-----------------------------
Melissa walking:
(1) +3+=+s%2At+
Melissa biking:
(2) +3+=+%28+s%2B4+%29%2A%28+2-t+%29+
-----------------------
(2) +3+=+2s+%2B+8+-+s%2At+-+4t+
(2) +3+=+2s+%2B+8+-+t%2A%28+s+%2B+4+%29+
and
(1) +t+=+3%2Fs+
By substitution:
(2) +3+=+2s+%2B+8+-+%283%2Fs%29%2A%28+s+%2B+4+%29+
(2) +2s+=+%283%2Fs%29%2A%28+s%2B4+%29+-+5+
Multiply both sides by +s+
(2) +2s%5E2+=+3%2A%28+s%2B4+%29+-+5s+
(2) +2s%5E2+=+3s+%2B+12+-+5s+
(2) +2s%5E2+%2B+2s+-+12+=+0+
(2) +s%5E2+%2B+s+-+6+=+0+
(2) +%28+s+-+2+%29%2A%28+s+%2B+3+%29+
(2) +s+=+2+ ( speed has to be positive )
Her walking speed is 2 mi/hr
-----------------------------
check:
(1) +t+=+3%2F2+
and
(2) +3+=+%28+s%2B4+%29%2A%28+2-t+%29+
(2) +3+=+%28+2%2B4+%29%2A%28+2-t+%29+
(2) +3+=+6%2A%28+2-t+%29+
(2) +1+=+2%2A%28+2-t+%29+
(2) +1+=+4+-+2t+
(2) +2t+=+3+
(2) +t+=+3%2F2+
OK

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
walking data
speed r
time t
distance 3
3=rt
cycling data
speed r+4
time 2-t because total time is 2.
distance 3
3=%28r%2B4%29%2A%282-t%29
solve the equations
3=rt
3=%28r%2B4%29%2A%282-t%29

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 2t%5E2%2B2t%2B-12+=+0) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A2%2A-12=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+100+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%282%29%2Bsqrt%28+100+%29%29%2F2%5C2+=+2
t%5B2%5D+=+%28-%282%29-sqrt%28+100+%29%29%2F2%5C2+=+-3

Quadratic expression 2t%5E2%2B2t%2B-12 can be factored:
2t%5E2%2B2t%2B-12+=+2%28t-2%29%2A%28t--3%29
Again, the answer is: 2, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-12+%29