A person leaves home at 8:00 a.m. and drives to a destination at a rate of 40 mph. The person returns at a rate of 25 mph and arrives at 2:30 p.m. If x represents how far it is to the destination, then which of the following expressions represents the amount of time to make the return trip?

Question

anonymous · Answer

@Compassionate

compassionate · Answer

Hello, there are a few simple ways to get the solution to this equation. Would you mind showing me the equations it has listed?

anonymous · Answer

Hi it didn't have an equation with the question.

compassionate · Answer

Okay, that is fine. I will tell you how to solve the word problem. 

First, you need to know the formula for average speed, which is: 

$$\frac{ 2xy }{ x + y }$$

By plugging the numbers given in: 

$$\frac{ 2 * 40 * 25 }{ 40 + 25 }$$

If he went there and back from 8:00 to 2:30, that means his time was 6.5 hours. 

That is: 40 = the rate you were originally going multiplied by the rate you came returning, divided by the rate you had coming and going combined. This formula works and it helps to memorize it. The next step is simplifying. 

You should get: 30.77

Now, this is asking for the TIME. So we can use the distance formula and plug in our variables. 
$$d = rt \rightarrow \frac{ d}{ r } = t$$
Note: Just like in the last equation, how I told you about equality, I took the distance formula: Distance equals rate times time, and solved it for time. That way, time equals distance divided by rate. 

Now, we know our average volecity is 30.77
We know his time is 6.5 hours. 

So: $$t = \frac{ 30.77 }{ 6.5 } \rightarrow t \approx 5.2$$

I hoped this helped. Come back to OpenStudy soon! We appreciate your contribution.