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

• roxas
So if you are using the quadratic formula, you would include the signs in the coefficients. In summary, the length of the route up the mountain is 20km and John followed it at xkm/h. He then came down a different route that was 25km long. His average speed coming down was 2km/h faster than his average speed going up, and it took him 1.5 hours less to come down than to go up. An equation in x is 3x^2 + 16x - 80 = 0. However, when trying to simplify it using the formula d = rt, it does not reduce to this equation.
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

Use $$d = rt$$

So: $$20 = xt$$

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

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?

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

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

Last edited:
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

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

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

okay thanks for ur help

The signs are part of the coefficients!

## 1. What is the purpose of "John's Mountain Trek"?

The purpose of "John's Mountain Trek" is to study the effects of varying speeds on a 45km journey. This trek will help scientists understand how different speeds impact the human body and overall performance.

## 2. How is the data collected during "John's Mountain Trek"?

During "John's Mountain Trek", data will be collected using various scientific instruments such as heart rate monitors, GPS trackers, and pedometers. The participants will also keep a log of their experience, including any physical and mental changes they may experience during the trek.

## 3. Who can participate in "John's Mountain Trek"?

Anyone who is physically fit and able to complete a 45km trek at varying speeds can participate in "John's Mountain Trek". Participants will undergo a screening process to ensure they meet the necessary physical requirements.

## 4. What are the potential benefits of "John's Mountain Trek"?

The potential benefits of "John's Mountain Trek" include a better understanding of how varying speeds impact the human body, improved physical fitness, and potential insights into how to optimize performance during long-distance journeys.

## 5. How will the results of "John's Mountain Trek" be used?

The results of "John's Mountain Trek" will be used to further research on human performance and inform training strategies for athletes and individuals engaging in long-distance activities. The data may also contribute to the development of new technologies and techniques for optimizing performance during physically demanding tasks.

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