MHB How long did the plane fly at 115 mph on a 246-mile trip with varying speeds?

[flnursegirl]

A plane makes a trip of 246 miles. For some amount of time the planes speed is 115 mph. For the remainder of the trip the planes speed is 250 mph. If the total trip time is 72 minutes, how many minutes did the plane fly at 115 mph?

 

[I like Serena]

A plane makes a trip of 246 miles. For some amount of time the planes speed is 115 mph. For the remainder of the trip the planes speed is 250 mph. If the total trip time is 72 minutes, how many minutes did the plane fly at 115 mph?

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? (Wondering)

 

[flnursegirl]

No can you show me more?

 

[topsquark]

No can you show me more?

Please be specific. What more help do you need? The derivation or solving the equation?

-Dan

 

[flnursegirl]

Need help to solve the word problem

 

[I like Serena]

Need help to solve the word problem

Erm... I've converted the word problem into an equation... (Thinking)
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? (Wondering)

 

[flnursegirl]

Could you show how to solve the equation?

 

[I like Serena]

Could you show how to solve the equation?

So the total distance is:
$$\frac{x}{60}\cdot 115 + \frac{72-x}{60}\cdot 250 = 246 \text{ miles}$$

Okay... it's like:

$$\frac{x}{60}\cdot 115 + \frac{72-x}{60}\cdot 250 = 246 \text{ miles} \\
\Rightarrow x \cdot \frac{115}{60} + \frac{72}{60}\cdot 250 - x \cdot \frac{250}{60} = 246 \\
\Rightarrow x\left(\frac{115}{60} - \frac{250}{60}\right) = 246 - \frac{72}{60}\cdot 250 \\
\Rightarrow x = \frac{246 - \frac{72}{60}\cdot 250}{\frac{115}{60} - \frac{250}{60}}
= \frac{246\cdot 60 - 72\cdot 250}{115 - 250}
= 24 \text{ minutes}
$$
(Emo)

 

[flnursegirl]

Thanks! I got it!