- Thread starter
- #1

#### flnursegirl

##### New member

- Jul 10, 2016

- 8

- Thread starter flnursegirl
- Start date

- Thread starter
- #1

- Jul 10, 2016

- 8

- Admin
- #2

- Mar 5, 2012

- 9,491

Hi flnursegirl! Welcome to MHB!

Let's call $x$ the number of minutes that the plane flew at 115 mph, which is what we want to know.

Then the distance the plane traveled in those $x$ minutes is:

$$\frac{x \text{ minutes}}{60\text{ minutes/hour}} \cdot 115 \frac{\text{mile}}{\text{hour}}$$

The distance the plane traveled in the remaining time is:

$$\frac{(72- x) \text{ minutes}}{60\text{ minutes/hour}} \cdot 250 \frac{\text{mile}}{\text{hour}}$$

So the total distance is:

$$\frac{x}{60}\cdot 115 + \frac{72-x}{60}\cdot 250 = 246 \text{ miles}$$

Can you solve that equation?

- Thread starter
- #3

- Jul 10, 2016

- 8

No can you show me more?

- Aug 30, 2012

- 1,264

Please be specific. What more help do you need? The derivation or solving the equation?No can you show me more?

-Dan

- Thread starter
- #5

- Jul 10, 2016

- 8

Need help to solve the word problem

- Admin
- #6

- Mar 5, 2012

- 9,491

Erm... I've converted the word problem into an equation...Need help to solve the word problem

That sort of solves the word problem doesn't it?

Do you need more help to solve the equation, or to understand how the word problem was converted into an equation?

What do you need help with exactly?

- Thread starter
- #7

- Jul 10, 2016

- 8

Could you show how to solve the equation?

- Admin
- #8

- Mar 5, 2012

- 9,491

Could you show how to solve the equation?

Okay... it's like:So the total distance is:

$$\frac{x}{60}\cdot 115 + \frac{72-x}{60}\cdot 250 = 246 \text{ miles}$$

$$\frac{x}{60}\cdot 115 + \frac{72-x}{60}\cdot 250 = 246 \text{ miles} \\

\Rightarrow x \cdot \frac{115}{60} + \frac{72}{60}\cdot 250 - x \cdot \frac{250}{60} = 246 \\

\Rightarrow x\left(\frac{115}{60} - \frac{250}{60}\right) = 246 - \frac{72}{60}\cdot 250 \\

\Rightarrow x = \frac{246 - \frac{72}{60}\cdot 250}{\frac{115}{60} - \frac{250}{60}}

= \frac{246\cdot 60 - 72\cdot 250}{115 - 250}

= 24 \text{ minutes}

$$

- Thread starter
- #9

- Jul 10, 2016

- 8

Thanks! I got it!