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

Hi Brent, if I calculate with Bill's speed = (Ted's speed) - 5 (B-5), I arrive at B = 20 , -15 not sure where did it go wrong?
B's speed = 240/ B-5
T's speed = 240/B + 4

240/ B-5 = 240/B + 4
240/ B-5 = (240 + 4B)/B
240B = (B-5)(240 + 4B)
240B = 240B + 4B^2 -1200 -20B
4B^2 -20B -1200 = 0
B - 5B - 300 = 0
(B-20) (B+15)=0
B = 20 , -15
gmat-admin's picture

I'm having a hard time following your solution.

If B = Bill's speed, then B + 5 = Ted's speed (since Bill's speed was 5 mph slower than Ted's speed, we can also conclude that Ted's speed was 5 mph greater than Bill's speed).

Are you letting B = Ted's speed?

Also, when you wrote "B's SPEED = 240/ B-5" did you mean Bill's travel TIME?

Since you got B = 20 mph as your answer, I'm assuming you have actually found Ted's speed, which would mean Bill's speed is 15 mph.

I suggest you try solving the question again, but be very careful with how you define speeds and times.

My bad Brent. Let me calrify it again as below and think I got the correct answer choice now?

T's speed = S
B's speed = S - 5 (since Bill's speed was 5 mph slower than Ted's speed)


T's time = 240/S + 4
B's time = 240/ S-5

240/ S-5 = 240/S + 4
240/ S-5 = (240 + 4S)/S
240S = (S-5)(240 + 4S)
240S = 240S + 4S^2 -1200 -20S
4S^2 -20S -1200 = 0
S^2 - 5S - 300 = 0
(S-20) (S+15)=0
S = 20 , -15

B's speed = S - 5 = 20-5 = 15

gmat-admin's picture

Perfect. Nice work!

Brilliant thanks Brent for confirmation.
One last question to clarify as noticed that your final answers are 15,-20 but mine are (20-5 = 15), -15.
Is there any issue with it and not sure why are they different? Thanks Brent
gmat-admin's picture

The differences in our solutions are caused by the fact that I created and solved an equation involving Bill's speed B, whereas you created and solved an equation involving Ted's speed S.

Got it thanks 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!

Question link: https://gmatclub.com/forum/each-type-a-machine-fills-400-cans-per-minute-each-type-b-machine-fill-220878.html

Hi Brent, can you please share your solution for this question?
gmat-admin's picture

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.
gmat-admin's picture

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?

Can I get the solution for this

https://gmatclub.com/forum/working-simultaneously-at-their-respective-constant-rates-m-143705.html

and the solution for this please

https://gmatclub.com/forum/during-a-trip-francine-traveled-x-percent-of-the-total-distance-at-an-94933.html

Can I get the solution for this one

https://gmatclub.com/forum/a-pump-started-filling-an-empty-pool-with-water-and-continue-73138.html
gmat-admin's picture

Tweet about the course!

If you're enjoying this GMAT 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 a GMAT expert will answer it as fast as humanly possible.

Free “Question of the Day” emails!