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## Comment on

Bill and Ted in a Race## Let T time ted complete the

Rate Time Distance

bob (240/T) - 5 T+4 240

ted 240/T T 240

Rate * Time = Distance

((240/T) - 5) ( T+4) = 240

240-5T+(960/T)-20 = 240

-5T^2+960-20T=0

T^2+4T-192 = 0

T can be -16 or 12 therefore T=12

now (240/12) - 5 = 12.

## I have a good feeling (based

I have a good feeling (based on your other solutions thus far) that your approach is valid :-)

However, in this solution, I'm not sure what you mean with some of the expressions. For example, I don't know what "(240/T) - 5 T+4 240" and "240/T T 240" are referring to.

## Thank you so much, Brent!,

Let T be the time Ted take to complete the race

Ted's rate => D/T = 240/T since 240 is the total distance.

Bob would be taking T+4 time to complete the race

Bob's rate will be 5 m/hr slower than Ted's rate, that is => (240/T) - 5

Bob's rate * Bob's time = distance

((240/T)-5) (T+4) ) = 240

240-5T+(960/T)-20 = 240

-5T^2+960-20T=0

T^2+4T-192 = 0

T can be -16 or 12 therefore T=12

Ted's race completion time is 12

Bob's rate will be (240/T) - 5 => ( (240/12) ) - 5 = 15 m/hr

## Perfect!

Perfect!

## What is the quicker strategy

## Hi Allison,

Hi Allison,

I agree with the fact that the GRE doesn't test our ability to perform long calculations. That said, this is a pretty high-level question, and the calculations (once you've created the equation) aren't that crazy.

## You said at the beginning of

## You bet.

You bet.

Let's test answer choice A) 7.5

This means Bill's average speed was 7.5 mph

Bill's travel time = distance/speed = 240/7.5 = 32 hours

We're told that Bill's speed is 5 mph slower that Ted's speed. So, Ted's average speed was 12.5 mph

Ted's travel time = distance/speed = 240/12.5 = 19.2 hours

The question tells us that Ted's travel time was 4 hours less than Bill's time.

HOWEVER, when we plug in answer choice A, Ted's travel time is 12.8 hours less than Bill's time

So, answer choice A is incorrect.

---------------------------------------

Now let's test answer choice E) 15

This means Bill's average speed was 15 mph

Bill's travel time = distance/speed = 240/15 = 16 hours

We're told that Bill's speed is 5 mph slower that Ted's speed. So, Ted's average speed was 20 mph

Ted's travel time = distance/speed = 240/20 = 12 hours

The question tells us that Ted's travel time was 4 hours less than Bill's time.

That's EXACTLY what we get when we plug in answer choice E!

So, answer choice E is correct.

## I solved it the same way as

## Keep in mind that you used B

Keep in mind that you used B and B-5 to denote the speeds, whereas I used B and B+5

Given this difference, we cannot expect our equations to be identical. Let's keep going with your equation:

You have: B² - 5B - 300 = 0

Factor: (B - 20)(B + 15) = 0

So, EITHER B = 20 or B = -15

Since the speed cannot be negative, the correct solution is B = 20

IMPORTANT: In your solution, you let B = TED's rate, and you let B-5 = BILL's rate.

Since, B = 20, we know that TED's rate is 20 miles per hour.

This means BILL's rate = 20 - 5 = 15 mph (which is the correct answer)

ASIDE: Be careful when assigning variables.

If you had let T = Ted's rate and T-5 = Bill's rate, you would have spotted the problem.

Cheers,

Brent

## Thank you so much Bent. Yes,I

## Hi,

Plz let me know if my approach is correct. Whenever the option's are values I try to fed the numbers to ques.

I start from option C: i.e.

Bill speed = 12

Therefore Bill's Time = 240/12 = 20

So Ted's time = 20 -4 = 16 and speed = 240/16 = 15, whereas Bill speed is 12 ( 12 + 5 =17) this is not possible

Similarly if I take Bill's speed as =15

therefore Bill's time = 16

And ted's speed = 20 , This is the answer because Bill's speed + 5 = 20 = Ted's speed.

I did left the decimal but I use to start from option C and deciding on the value either move to E or A.

## That approach is perfect.

That approach is perfect. Nice work!

Cheers,

Brent

## I approached this question

Bill: Avg speed = x - 5 , time = t

distance = speed x time

time = 240/*(x-5)

Ted: Avg speed = x, time = t-4

distance = speed * time

time = 240/x + 4

Now my confusion starts. In the previous videos, I saw that we need to make the times equal to solve the equation. So let's write what I learnt and recall

240/(x-5) = 240/x + 4 + (4)-> This additional 4 is for the difference to equalize the time. But this gives the incorrect answer

If i solve the question like : 240/(x-5) = 240/x + 4 then I get the correct answer. Can you please explain what am I doing wrong?

## You did a lot of things

You did a lot of things correctly in your solution. However, there are two errors.

Early in your solution, you say that Ted's time = 240/x + 4

This is not true.

Travel time = distance/speed

Ted's distance is 240 miles, and his speed is x mph

So, his travel time = 240/x

IMPORTANT: At this time, we aren't yet trying to create an equation. So, we don't yet need to add 4.

To avoid this from happening, you should START with a word equation.

You have decided to equate their travel times.

So, we can write: (Bill's travel time) = (Ted's travel time) + 4

NOTE: NOW it's our goal to create an EQUATION. To create equality, we must add 4 hours to Ted's travel time.

Now that we have our EQUATION in place, it's just a matter of filling in the blanks.

time = distance/rate

Distance = 240 miles (for each person)

Bill's speed = x - 5

Ted's speed = x

So, we can write: 240/(x-5) = (240/x) + 4

Does that help?

Cheers,

Brent

## Hello Brent!

If there is any way to find the values of Xs

In this case 30 and 20

Instead of applying the formula ?

Thanks ! :)

## If by "formula" you mean the

If by "formula" you mean the distance/rate/time formula, then the answer is "no, we need to use that formula"

Does that help?

Cheers,

Brent

## The absolute hardest thing

## If you're not certain whether

If you're not certain whether you need to ADD or SUBTRACT, plug in some values that satisfy the given information and then determine what you need to do to make those quantities equal.

For example: Joe is 3 years older than Sue.

Let J = Joe's present age, and S = Sue's present age

So, it could be the case that J = 13 and S = 10

At this point, in order to create an equation, we must EITHER add 3 years to Sue's age OR subtract 3 years from Joe's age.

## Hello Brent,

Just to see another approach could we use average speed in this problem.

The way i set it up was 240/[(240/x-5)+240/x)] = (x-5) and then use this so solve for x.

Although this is a long approach and using the Answer choices is by far the best method, i just want to see if I have the right equation setup. Thanks.

## Hi Ravin,

Hi Ravin,

Unfortunately this approach won't work.

Your denominator, [240/x-5) + 240/x] represents the COMBINED travel times of Bill and Ted.

If you want to use average speed, then the numerator would have to be 480 miles to represent the COMBINED distance traveled by Bill and Ted.

So, 480/[(240/x-5)+240/x)] represent Bill and Ted's average speed.

Unfortunately, don't have a problem since we don't know their average speed.

In your solution, you are saying that their average speed is x-5, but this represents Bob's speed only.

## I set up my equation as

RT = 240 for Ted

(r-5)(t+4) = 240 for Bob and set them equal

rt= (r-5)(t+4)

rt = rt + 4r - 5t -20

20 + 5t = 4r

I don't know how to keep solving or if I am making incorrect assumptions?

## The problem with your

The problem with your solution is that you're not actually using the fact that both men traveled 240 miles.

Notice that, if we made one small change to the question and said the men traveled 240,000,000, your resulting equation would still be the same: 20 + 5t = 4r

When you have rt = 240 ( where r and t = Ted's rate and time), you can convert this to t = 240/r, which means t = 240/r

Now we're using the fact that both men traveled 240 miles.

Likewise, if we know that (r-5)(t+4) = 240 (where r-5 and t+4 = Bob's rate and travel time), we can also write: t+4 = 240/(r-5)

Or we can write: t = 240/(r-5) - 4

At this point we have two equations that are both set equal to t, which means we can write: 240/r = 240/(r-5) - 4

Does that help?

## yes! So I must use some form