How Can John's Mountain Trek Equation Simplify to 3x² + 16x - 80 = 0?

[roxas]

a route up a mountain is 20km
john followed this route at xkm/h
he came down a different route
the length of the route is 25km
his average speed coming down increase by 2km/h than his average speed going up
it took john 1.5 hours less to come down than to go up
write an equation in x and show it simplifies to

3x^2 + 16x - 80 = 0

i tried doing it, but i can't reduce it to this equation. can anyone help me

i basically did this

20/x - 1.5 = 25/x+2

it can't reduce to the above equation. please help me. thx

 

[courtrigrad]

Use $$d = rt$$

So: $$20 = xt$$

$$25 = (x+2)(t-1.5)$$

 

[roxas]

thx so much. one more think i need to ask, if i put the conefficients into the quadratic formula, do i have to include the + - signs into it, or do i just use the numbers?

 

[courtrigrad]

I am not sure I understand your question. You have to use the + and - in the quadratic formula.

$$x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$$

 

[roxas]

if its 5x^2 + 16x - 50 = 0

and i sub it into the quadratic formula, do i just sub in the coefficients only, or do i have to include the signs.


for my first question i tried it, but i ended up having

8x + 1.5x -40 = 0
i don't know i i did wrong

 

[courtrigrad]

If $$5x^{2} + 16x - 50 = 0$$ then

$$x = \frac{-16\pm \sqrt{16^{2}-4(5)(-50)}}{10}$$

 

[roxas]

okay thanks for ur help

 

[HallsofIvy]

The signs are part of the coefficients!