Question: Traveling at x Miles Per Hour

Comment on Traveling at x Miles Per Hour

When you are comparing 300 with 600, do you need to take units into account? In this case, wouldn't it be 300 hours vs 600 minutes?
greenlight-admin's picture

The question is asking us to compare the number of hours (say j) with the number of minutes (say k). So, we need not consider the fact that 300 hours is actually longer than 600 minutes. We need only recognize that j (which has value 600) is greater than k (which has value 300).

That said, IF the question were worded such that we were comparing the length of time only, then quantity A would be greater.

What if X is 1000 mile/hour?
Wouldn't that be 300/1000 > 600/1000?
greenlight-admin's picture

You're right in that Quantity A would be 300/1000 and Quantity B would be 600/1000.
However, 300/1000 < 600/1000 (not the other way around). So, the correct answer is still B.

OMG yes.
I am Sorry, I need to take a break :D
greenlight-admin's picture

It happens to everyone :-)

Hello, can you please explain how 10/x/60 becomes 600?
I thought it will be 10/x * 1/60 = 10/60x
sorry. I think I am missing something. thanks
greenlight-admin's picture

Hi senyo,

Be careful; you are simplifying a quotient that's different from the quotient in the video question.

In the video solution, we start with 10 in Quantity B, and then we divide that amount by x/60.

So, we get: 10/(x/60) = (10)(60/x) [invert and multiply]
= (10/1)(60/x)
= 600/x

In your calculations, you are simplifying the quotient (10/x)/60, when you should be simplifying 10/(x/60)

Your calculations are correct mind you. The only problem is that you are evaluating the wrong expression.

Does that help?


Thank you. That helps a lot

why do we use 600/x and not 60t as the time variant
greenlight-admin's picture

My answer to your question largely depends on what t represents.
If t = the travel time (in hours), then 60t = the travel time in minutes.
However, this doesn't really help us here, since each quantity is providing information about speeds and distances, and our goal is to calculate the time.

As such, we don't really need to add any additional variables.
We need only use the fact that time = distance/rate.

So, for Quantity B, we must convert the speed, x miles per hour, to a rate in terms of miles per MINUTE.

If my speed is x miles per HOUR, then I will travel x miles every hour.
In other words, I'm traveling x miles every 60 MINUTES.
So, in ONE MINUTE, I travel x/10 miles
So, x miles per hour = x/60 miles per minute.

Once I've made this conversion, we'll apply the time = distance/rate formula to Quantity B.

Does that help?


Can we just substitute a value for x and do it? For example 5 miles.
greenlight-admin's picture

That's a perfect (and very fast) approach!

Wouldn't A be greater, if x was 10 miles per hour?
greenlight-admin's picture

If x = 10 mph, we get:
QUANTITY A: time = 300/10 = 30 (hours)
QUANTITY B: time = 10/10 = 1 hour = 60 (minutes)
Quantity B is greater.

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