# GMAT Work and Rate Problems Mini-Course (with Videos!)

## GMAT Work and Rate problems might seem like a pain in the ass, but they don’t have to be.

The fact that these questions look worse than they truly are just comes down to over-complicated methodology and dubious pedagogy.

This little group of videos is here to teach you a new way to think about GMAT Rates questions–one that is intentionally flexible so that you will be able to apply these short lessons to live GMAT Work questions.

GMAT Work and Rates Mini Video Course

### GMAT Rates Video 1: Bob Does Pointless Things Down by the River

After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?

(A) 1.5 (B) 2.25 (C) 3.0 (D) 3.25 (E) 4.75

What’s special about this type of GMAT Work and Rate problems? I’ve chosen it specifically because it’s a question that annoys the crap out of people because it has a lot of back-and-forth.

First, note the rate: 8 minutes per mile. (Note that there’s something awkward about this. We’ll deal with it later.)

Second, it’s easiest just to draw a picture to figure out what the question itself is actually talking about.

That is, notice that Bob actually travels a certain distance–then looks at his watch, noting that he needs to be back to his car in 50 minutes–then keeps going in the same direction! It’s really quite odd. If he knows he needs to be home soon, why not just turn around?

Because this is a GMAT question.

### So set it up as in the video: start the clock where Bob looks at his watch.

That first 3.25 miles is actually irrelevant. The distance that he travels farther south is our variable, x.

Therefore, he travels x miles farther south and 3.25 + x miles back to his car. That’s our distance.

Third, Plug it all into d = r * t.

Notice that our rate of 8 minutes per mile won’t work because the units don’t cancel properly. Rather, we’ll have to change this to 1⁄8 miles per minute (remember, for d = r*t, a rate will always be distance/time).

### REMEMBER: ALWAYS CHECK YOUR UNITS.

Now this all works out. Just algebra from this point–with a little bit of adjusting the numbers by converting decimals to fractions, we get the answer as x = 3/2 miles = 1.5 miles.

Click the video for the full explanation…

### GMAT Work and Rate Problems Video 2: The One Where You NEED to Calculate

Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.

A. 4 B. 6 C. 8 D. 10 E. 12

What’s special about this Rates question? I’ve chosen it specifically because it’s one that is totally achievable–the setup isn’t even that bad–but it will likely take 3-4 minutes to calculate.

Is that feasible on the GMAT? Depends on how solid your Algebra is. First, note the rate for each machine:

Rate X: w/(d+2) widgets/day

Rate Y: w/d widgets/day

Combine the rates, then plug into d = r*t, just as we’ve been doing in the book.

That’s easier said than done, but on the other side of that ugly quadratic, you’ll find d = 4. That means d + 2 = 6 would be the time for x1.

Now we know that x produces w widgets in 6 days, so it follows that x produces 2w widgets in 12 days. Your answer is E.

Check the video for a full explanation…

### GMAT Work and Rates Video 3: If It Looks Easy, It Might Actually be Easy

Jonah drove the first half of a 100-mile trip in x hours and the second half in y hours. Which of the following is equal to Jonah’s average speed, in miles per hour, for the entire trip?

A. 50/(x + y)

B. 100/(x + y)

C. 25/x + 25/y

D. 50/x + 50/y

E. 100/x + 100/y

I have to admit, the first time I looked at this, I had to do a double-take. There must be something else required of us, right?

Then I looked back and realized that actually, no, they give us total distance (100 miles) and total time (x hours + y hours) and that’s actually all we need to solve an Average Rate question.

Sometimes the key to a GMAT question is to realize when to stop. If you’re confident in what it says and that you’re doing no more or no less than what it’s asking, you’ll be fine.

Was that explanation too short? Check the video for details:

https://youtu.be/mge9Qybz7P4

## GMAT Work and Rate Problems Video 4: Too Many Variables!

A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?

(a) 2 mph

(b) 3 mph

(c) 4 mph

(d) 5 mph

(e) 6 mph

What’s special about this GMAT Rates question? It really looks like there are too many variables for this question to work correctly.

Let’s just step back and take a deep breath…

OK–notice that we can relate the “two hours longer” and the “one mile per hour faster.” That’s a start.

Still, we’re left with two variables. We’ll need another equation to make this work properly.

Any ideas? What can we do?

Well, we have the total distance… and the total time! That means we actually have the Average Rate as the answer. That means the thing that we normally don’t have is actually simply given to us. (Still, remember we’re looking for Day 1’s Average Rate).

### Again, the GMAT has presented it backward to try to confuse us. Uggh.

How can you solve this? Take good notes and make sure you take advantage of the information given. If you see that we have enough to cook up the Average Rate for the whole thing, you’ll see that we can solve the question.

Take a look at the video…

### GMAT Work and Rates Video 4: Does it Really Make Sense to Plug In? (Answer: no.)

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine’s

average speed for the entire trip?

(a) (180−x)/2
(b) (x+60)/4
(c) (300−x)/5
(d) 600/(115−x)
(e) 12,000/(x+200)

What’s special about this particular GMAT Rates question? This one is just about as complicated as a GMAT Average Rates question can get.

Another thing to note is that it would be completely pointless to do this question by plugging numbers in.

How can I tell that easily?

First, I’m wary of plugging numbers in on the GMAT and I would only do it in situations where we can easily insert ANSWER CHOICES to test.

Second, just look at the answers! Your answers have variables in them, which means you need to just work with variables.

All it takes is a bit of practice with Algebra. In reality, once you’re sufficiently confident with Algebra, I’d wager you’ll find that it’s easier to work with variables than actual numbers. Leave that to your accountant.

Enjoy!

### GMAT Work and Rates Video 6: How to Organize a Rates Question on the Basis of Units

A certain manufacturer sells its products to stores in 113 different regions worldwide, with an average (arithmetic mean) of 181 stores per region. If last year these stores sold an average of 51,752 units of the manufacturer’s product per store, which of the following is closest to the total number of units of manufacturer’s product sold worldwide last year?

(a) 10^6

(b) 10^7

(c) 10^8

(d) 10^9

(e) 10^10

What I mean is that in this case, all you need is to establish the Units and figure out how you make them relate to one another.

By analyzing how the Units relate to one another–aiming to get an answer in a total number of units sold–you’ll be able to figure out, in each case, whether to multiply or divide (“divide” meaning flip and multiply based on units) such that your final Unit ends up as units sold.

(“Unit” used to discuss our major concept here; “unit” used to discuss “total units sold” as in the question).

Enjoy!

Click the video for the full explanation…

### GMAT Work and Rates Video 7: The Worst Units Question You’re Likely to See

A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of p square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)

(a) 5280mt/12p

(b) 5280pt/12m

(c) 5280pmt/12

(d) (5280x12m)/pt

(e) (5280x12p)/mt

Bear in mind that you’ll need to do lots and lots of conversions in this one. I’d suggest converting first miles and inches both to ft and then multiply ft by ft in order to get ft^2.

Click the video for the full explanation…

### GMAT Work and Rates Video 8: A Wacky Way to Split Up Time

Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system?

(a) 1:00 p.m.

(b) 2:00 p.m.

(c) 3:00 p.m.

(d) 4:00 p.m.

(e) 5:00 p.m.

What’s special about this GMAT Rates question? Time, time, time. Not just one time will do, so not just one d = r x t will do!

We need to figure out what the specifics here are for Al’s time and Ben’s time separately, and then we need to figure out how to equate them as a final step.

Click the video for the full explanation…

## If you’ve enjoyed the explanations thus far, check out the GMAT Work and Rates Guide here:

How to Beat GMAT Work and Rates Problems