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?
Thanks
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?

http://www.beatthegmat.com/ds-french-japanese-t222297.html
gmat-admin's picture

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 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?

Cheers,
Brent

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

Right?
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?

Cheers,
Brent

https://gmatclub.com/forum/will-laurie-get-to-the-apartment-building-before-ernest-if-they-both-239835.html
please explain
gmat-admin's picture

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-train-traveling-at-72-kmph-crosses-a-platform-in-30-seconds-and-a-ma-215070.html
please explain

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
gmat-admin's picture

Nice work!

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