Question: Cole’s Travel Time

Comment on Cole’s Travel Time

here's a nice one. Whenever we are presented either with the ration of speed or with the ratio of time, we can use the concept that the ration of speed is reciprocal to the ratio of times. since we are asked on the time it took Cole to drive from home to work, we can say the following: Speed ratio - 75:105 = or 5:7 and thus the time ratio is reciprocal which is 7:5. since the total time is 2 hours = 120 minutes - then 120 min = 12 units (7+5) therefore - 7 units = 70 min. this is the correct answer. WDYT?
gmat-admin's picture

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

I did is calculate total distance with speed as distance is same . I 75+105 is 180 /2 avg speed is 90 . We know 2 hours is total so speed into time is 180km is distance so half of this is one side . So we know speed and distance . 90/75 equal to 1.2 hours *60 to get into 72 min
gmat-admin's picture

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 Brent

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
gmat-admin's picture

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 from home to work and not the opposite from work to home.

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?
gmat-admin's picture

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.
gmat-admin's picture

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 you set W = Time driving to work and (2-W)=Time driving to home.

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.



gmat-admin's picture

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 this but my calculations gave me 72 mins:

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?
gmat-admin's picture

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

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