Question: Bill and Ted in a Race

Comment on Bill and Ted in a Race

A the beginning of the video you said we can check for the answer choices. How do we do that?
gmat-admin's picture

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 question!
gmat-admin's picture

I'm glad you like it!

Hi Brent,
Could you show me the step by step solution for this problem using double matrix method?
gmat-admin's picture

The first solution here uses the Double Matrix method.

From where did you got the number 260? The question says that the race was for 240 miles
gmat-admin's picture

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?


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

gmat-admin's picture

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?

please explain
gmat-admin's picture

That question is not really GMAT-worthy.
Here's my full solution:

please explain

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

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
gmat-admin's picture

Nice work!

Add a comment

Tweet about the course!

If you're enjoying my video course, help spread the word on Twitter.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

Free “Question of the Day” emails!