# Question: Bill and Ted in a Race

## Comment on Bill and Ted in a Race

### A the beginning of the video

A the beginning of the video you said we can check for the answer choices. How do we do that?
Thanks ### Let's test one answer choice

Let's test one answer choice together.

B) 10
This means Bill's average speed is 10 miles per hour (mph).
Since Bill's speed is 5 mph slower than Ted's speed, we know that Ted's speed is 15 mph.

Travel time = distance/speed

So, Bill's travel time = 240/10 = 24 hours

Ted's travel time = 240/15 = 16 hours

So, we can see that Ted's travel time is 8 hours less than Bill's travel time.

These times do not match the information in the question, which says Ted's travel time is 4 hours less than Bill's. So, we need to check more answer choices.

### Once again! An excellent

Once again! An excellent question! ### Hi Brent,

Hi Brent,
Could you show me the step by step solution for this problem using double matrix method?

http://www.beatthegmat.com/ds-french-japanese-t222297.html ### The first solution here http:

The first solution here http://www.beatthegmat.com/at-least-100-students-at-a-certain-high-schoo... uses the Double Matrix method.

### From where did you got the

From where did you got the number 260? The question says that the race was for 240 miles ### I believe you're referring to

I believe you're referring to 3:13 in the video.

If so, we got 260 + 4B on the right side of the equation after we simplified the expression 240 + 4B + 20.

Does that help?

Cheers,
Brent

### i didn't get it. I fthe

I didn't get it.
If the average speed of Bill is slower, then the Speed of Bill = (Speed of Ted) - 5.

Right? ### I believe you're referring to

I believe you're referring to the point at 1:15 when I say that (Bill's speed) + 5 = Ted's speed.

This equation is EQUIVALENT to your suggested equation: Bill's speed = (Ted's speed) - 5

In fact, if we take your equation: Bill's speed = (Ted's speed) - 5
And add 5 to both sides to get: (Bill's speed) + 5 = Ted's speed, which is my equation.

Does that help?

Cheers,
Brent

### https://gmatclub.com/forum

https://gmatclub.com/forum/will-laurie-get-to-the-apartment-building-before-ernest-if-they-both-239835.html ### That question is not really

That question is not really GMAT-worthy.
Here's my full solution: https://gmatclub.com/forum/will-laurie-get-to-the-apartment-building-bef...

Cheers,
Brent

### https://gmatclub.com/forum/a

https://gmatclub.com/forum/a-train-traveling-at-72-kmph-crosses-a-platform-in-30-seconds-and-a-ma-215070.html ### This is my approach, but I

This is my approach, but I don't think its any better.

Givens:
240 = vb * tb = vt * tt
vb + 5 = vt
tt + 4 = tb

Solve for vb
vb * tb = vt * tt
vb * tb = (vb + 5) * (tb - 4)
vb * tb = vb * tb + 5tb - 4vb - 20
4vb + 20 = 5tb
4vb + 20 = 5 * 240/vb
vb^2 + 5vb - 300 = 0
(vb + 20) * (vb - 15) = 0
vb = 15 ### Nice work!

Nice work! ### Hi Brent,

Hi Brent,

I struggled with the arithmetic approach so I decided the go with the Put-in numbers approach, starting with C.

So, if RateB= 12 then TimeB must be 20h, ergo TimeT must be 16h. If we check 240/16, that equals RateT to be 15. RateB-RateT=3 =/= 5. Eliminate answer C.

Then I went for an easy integer such as the one found in answer E to repeat the same operation, which is the correct answer.

My question is the following - how should I choose the next value after I discarded answer C.

Meaning, the difference between Rates in answer C was 3 (not 5 as the statement says) but I really did not know whether to choose a smaller value (for instance that of answer B) or to choose a bigger value (for instance answer E).

Thank you. ### Here's the key concept at

Here's the key concept at play here.

Notice that, the closer bills speed gets to 5 mph,the greater the RELATIVE speeds between the two people.

For example, if Bill's speed = 6 mph, then Ted's speed is 1 mph, which means Bill's speed is SIX TIMES that of Ted's speed.

For example, if Bill's speed = 10 mph, then Ted's speed is 5 mph, which means Bill's speed is TWO TIMES that of Ted's speed.

For example, if Bill's speed = 25 mph, then Ted's speed is 20 mph, which means Bill's speed is 1.25 TIMES that of Ted's speed.

Now let's test answer choice C:
If Bill's speed = 12 mph, then Ted's speed is 7 mph, which means Bill's travel TIME is 20 hours and Ted's travel time is about 34 hours.

Since we need a time difference of only 4 hours, we want their relative speeds to be closer to each other.
As such, we need their speeds to be greater.
So, we can eliminate answer choices A, B and C

Does that help?