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## Comment on

Cole’s Travel Time## here's a nice one. Whenever

## That's a valid approach. That

That's a valid approach. That said, I avoid teaching it, because I think it confuses too many students.

## I did is calculate total

## That solution is incorrect,

That solution is incorrect, because we cannot find the average speed by calculating the average of the two speeds.

For more on this, watch: https://www.gmatprepnow.com/module/gmat-word-problems/video/911

## HI Bret

By using the logic of the previous video, why does my solution not work when I use the approach Travel Time to Work + Travel Time Home = 2 hours not yield a good result?

So

TIMEw + TIMEh = 2 hours

d/75 + d/105 = 2 hours

105D + 75d = 2(75 x 100) and so on

Am I missing a key bit of logic or solution method here?

Thanks and regards

## Your solution is perfect up

Your solution is perfect up to the point where get to d/75 + d/105 = 2 hours

The next step SHOULD read 105D + 75d = 2(75 x 105) [you have 100]

Simplify: 180d = (150)(105)

Solve: d = (150)(105)/180

d = (5)(105)/6

d = 87.5

So, time to work = distance/speed

= 87.5/75 hours

= 175/150 hours

= 7/6 hours

= 70 minutes

## How do I know it is .. 2-W

If I apply it in another variable 2-H lets say from work to home it leaves me with 5/6. How do I know is 2-W instead of 2-H?

## Good question.

Good question.

Your question illustrates the importance of being very clear what values your variables represent.

In my video solution, I let W = the time spent driving to WORK

Since the total driving time is 2 hours, I concluded that 2-W = the time spent driving to HOME.

However, I COULD have also let H = the time spent driving to HOME, in which case 2-H = the time spent driving to WORK.

Either approach will yield the correct solution.

In the second approach (where we let H = the time spent driving to HOME), we would conclude that H = 5/6 hours. This means the time spent driving to HOME = 5/6 hours.

Since 2-H = the time spent driving to WORK, then 2 - 5/6 = the time spent driving to WORK

Having said all of that, the question asks us to find the time spent driving to WORK. So, it's not a bad idea to assign the variable to equal the value we're trying to determine.

Does that help?

Cheers,

Brent

## Hello Brent,

I followed the ratio approach 75/180=x/2

But the answer with this approach is 50 mins.

I'm not being able to identify the mistake with this approach. Let me know what you think about its validity.

Regards.

## That approach won't work.

That approach won't work.

Your (presumed) rationale is that, since the COMBINED speeds is 180 kmh, then the TIME spent driving slower speed is proportionate to 75 kmh and the COMBINED speeds. Under this rationale, Cole spends LESS TIME traveling 75 kmh than he spends traveling 105 kmh.

However, the exact opposite is true: the slower your speed, the GREATER your travel time. For example, if I drive 100 km at a speed of 1 kmh, my travel time will be greater than my travel time had I driven at 50 kmh.

Cheers,

Brent

## Hi Brent, I get confused when

I tried to use H = Time driving home and (2-H)=Time driving to work. Shouldn't this logically work because we do not know our individual times. All we know is that the total time is 2 hours.

With my approach I get:

75(2-H)=105H

150-75H=105H

150=180H

H=150/180

H=5/6

This would result in a different answer, unless I am mistake.

## Your solution is perfect.

Your solution is perfect.

H = Time driving home

If H = 5/6, then it takes 5/6 hours to drive HOME.

The question asks us to determine the time to drive TO WORK.

You've already stated that (2 - H) = time driving to work

So: (2 - 5/6) = time driving to work

So: 7/6 hours = time driving to work

7/6 hours = 70 minutes.

Cheers,

Brent

## I set up an RTD table for

R T D

75 x d

105 y d

75x = 105y

5x = 7y

x + y = 2

Did I set it up wrong or were my calculations incorrect? Also, there is absolutely no way that I would be able to read the question work through the math in under 2 mins. Is there a much quicker way to tackle these problems on test day?

## Your approach is perfectly

Your approach is perfectly valid.

You have the following:

5x = 7y

x + y = 2

When you solve the above system of equations, you get x = 70 minutes

This type of question can be time-consuming. So, you need to start creating equations as soon as possible.

If you keep practicing these kinds of questions, your speed will improve.

Cheers,

Brent

## Great video Brent. One

## Given: The round trip took a

Given: The round trip took a TOTAL of 2 hours.

In other words: (travel time to work) + (travel time to home) = 2

We can use this equation to confirm any variables we assign.

In your solution, you have:

W = travel time to work

W - 2 = travel time to work

When we add these values, we get W + (W - 2), which doesn't necessarily add to 2 hours.

In my solution, we have

W = travel time to work

2 - W = travel time to work

When we add these values, we get W + (2 - W), which definitely adds to 2 hours.

When assigning variables, you can start with a word equation.

The word equation here is: (travel time to work) + (travel time to home) = 2

So, if W = travel time to work, we now have: W + (travel time to home) = 2

From here, we can subtract W from both sides of the equation to get: travel time to home = 2 - W

Does that help?

## Great explanation always and