SOLUTION: This question I come up with the wrong answer: Pete drove from Buffalo to Boston, a distance of 720km. On return trip he increased his speed by 10km/h. If the total trip took 17h

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: This question I come up with the wrong answer: Pete drove from Buffalo to Boston, a distance of 720km. On return trip he increased his speed by 10km/h. If the total trip took 17h      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 214899: This question I come up with the wrong answer:
Pete drove from Buffalo to Boston, a distance of 720km. On return trip he increased his speed by 10km/h. If the total trip took 17h, what was his speed from Boston to Buffalo?
I'm having trouble working it out, I begin with this:
I start with (720/x)+(720/x+10)
Expanded it to: 17x^2 - 1270x + 7200
Speed I got next using the quadratic equation: 62.5
But thats apparently wrong, what am I doing wrong?
Found 3 solutions by Alan3354, stanbon, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Pete drove from Buffalo to Boston, a distance of 720km. On return trip he increased his speed by 10km/h. If the total trip took 17h, what was his speed from Boston to Buffalo?
----------------
(720/r) + 720/(r+10) = 17
720r + 720(r+10) = 17r*(r+10)
1440r + 7200 = 17r^2 + 170r
17r^2 - 1270r - 7200 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 17x%5E2%2B-1270x%2B-7200+=+0) has the following solutons:

x%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=%28-1270%29%5E2-4%2A17%2A-7200=2102500.

Discriminant d=2102500 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1270%2B-sqrt%28+2102500+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1270%29%2Bsqrt%28+2102500+%29%29%2F2%5C17+=+80
x%5B2%5D+=+%28-%28-1270%29-sqrt%28+2102500+%29%29%2F2%5C17+=+-5.29411764705882

Quadratic expression 17x%5E2%2B-1270x%2B-7200 can be factored:
17x%5E2%2B-1270x%2B-7200+=+%28x-80%29%2A%28x--5.29411764705882%29
Again, the answer is: 80, -5.29411764705882. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+17%2Ax%5E2%2B-1270%2Ax%2B-7200+%29

r = 80 km/hr Boston to Buffalo
r = 90 km/hr return

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Pete drove from Buffalo to Boston, a distance of 720km. On return trip he increased his speed by 10km/h. If the total trip took 17h, what was his speed from Boston to Buffalo?
I'm having trouble working it out, I begin with this:
I start with (720/x)+(720/x+10)
Expanded it to: 17x^2 - 1270x + 7200
Speed I got next using the quadratic equation: 62.5
But thats apparently wrong, what am I doing wrong?
---------------------------------------------------
Buff to Bost DATA:
distance = 720 km ; rate = x km/h ; time = d/r = 720/x hrs
----------------------------------------------------------
Bost to Buff DATA:
distance = 720 km ; rate = x+10 km/h ; time = 720/(x+10) hrs
--------------------------------------------
Equation:
time + time = 17 hrs.
(720/x) + (720/(x+10)) = 17
Multiply thru by x(x+10) to get:
720(x+10) + 720(x) = 17x(x+10)
720x + 7200 + 720x = 17x^2 + 170x
17x^2 - 1270x - 7200 = 0
(x-80)(17x + 90) = 0
Positive solution:
x+ 10 = 90 km/h (rate from Boston to Buffalo)
================================================
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I write 2 equations, 1 for each
leg of the trip.
Buffalo to Boston:
d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
given:
d%5B1%5D+=+720 km
d%5B2%5D+=+720 km
r%5B2%5D+=+r%5B1%5D+%2B+10 km/hr
t%5B1%5D+%2B+t%5B2%5D+=+17 Hr
-----------------------
I can rewrite the equations
720+=+r%5B1%5D%2At%5B1%5D
t%5B1%5D+=+720%2Fr%5B1%5D
and
720+=+%28r%5B1%5D+%2B+10%29%2At%5B2%5D
720+=+%28r%5B1%5D+%2B+10%29%2A%2817+-+t%5B1%5D%29
720+=+17r%5B1%5D+%2B+170+-+r%5B1%5Dt%5B1%5D+-+10t%5B1%5D
By substitution:
720+=+17r%5B1%5D+%2B+170+-+720+-+10t%5B1%5D
720+%2B+550+=+17r%5B1%5D+-+10%2A%28720%2Fr%5B1%5D%29
Multiply both sides by r%5B1%5D
1270r%5B1%5D+=+17%2A%28r%5B1%5D%29%5E2+-+7200
17%2A%28r%5B1%5D%5E2%29+-+1270r%5B1%5D+-+7200+=+0
Using quadratic equation:
r%5B1%5D+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+17
b+=+-1270
c+=+-7200

r%5B1%5D+=+%28+1270+%2B-+sqrt%28+1612900+%2B+489600+%29%29%2F+34+
r%5B1%5D+=+%28+1270+%2B-+sqrt%28+2102500+%29%29%2F+34+
r%5B1%5D+=+%28+1270+%2B-+1450%29%2F+34+
r%5B1%5D+=+2720%2F34
r%5B1%5D+=+80 km/hr
His speed from Buffalo to Boston was 80 km/hr
check:
r%5B2%5D+=+r%5B1%5D+%2B+10 km/hr
r%5B2%5D+=+90 km/hr
720+=+r%5B1%5D%2At%5B1%5D
720+=+80%2At%5B1%5D
t%5B1%5D+=+9 hr
t%5B2%5D+=+17+-+9
t%5B2%5D+=+8
and
720+=+90%2A8
720+=+720
OK
It looks like you had a sign wrong