## Interview Question

Trader Interview New York, NY

`Morgan Stanley`

## If two cars are traveling in a two lap race on a track of

any length, one going 60 mph and the other going 30mph, how fast will the slower car have to go to finish at the same car to finish at the same time?

## Interview Answer

28 Answers

the answer to this question lies on how long the race track, we can solve its mph if we know how long the track we be.

Well, this is interesting because there are no track details and makes for multiple answers through ambiguity and assumptions. i.e. One could assume that it is a circular track and that the two lanes are very wide and that one car is on the outermost furthest from the centre and the other is on the track very near the centre. The circumference of each track therefore could be such that the faster car would have to travel twice the distance that the slower car has to and therefore the two cars would arrive at exactly the same time. The is why cares on a racetrack must start at offsets to each other or have their times corrected in some other way!

In real-life, this is highly unlikely however it does demonstrate my point.

I agree with the first answer (by the Interview Candidate). When the slow car completes the first lap, the fast will complete the second lap. It does not matter how fast the slow car goes on the second lap; it cannot win...

90 mph

Wouldn't the slow car just need to go 60mph? It doesn't say that the fast car is going double the slow cars speed only that the slow car is going 30 mph and the fast is going 60mph.

The question is a trick. It says how fast will the slower car have to go to finish "AT THE SAME CAR" to finish at the same time? It can go any speed!! It will always finish at the same car (2nd) at the same time. The car isn't changing!!!

I'm assuming that the question, as typed, was entered incorrectly and that it should be worded, "How fast will the slower car have to go to finish at the same time as the faster car?"

The answer is 30mph. Because that's how fast the slower car is going. Nowhere in the question does it state that the cars are at the same point on the track. The slower car is currently halfway between the faster car and the end of the race.

The two pieces of missing info are: 1. How long is the distance of the track and 2. The distance that each of the cars has already traveled on the track.

If you have that info then you can figure it out.

The two pieces of missing info are: 1. How long is the distance of the track and 2. The distance that each of the cars has already traveled on the track.

If you have that info then you can figure it out.

I totally agree with wildfire.

Did you just say, "If two cars are traveling in a two lap race on a track of any length, one going 60 mph and the other going 30mph, how fast will the slower car have to go to finish at the same car to finish at the same time?" WTF? Are you having a stroke? Try to raise both hands above your head. OK, now smile for me. And would you please try to say a complete sentence?

The way the question is currently worded, it does not indicate any of the following:

1. Whether the two cars started at the same place, at the same time (we can infer "same place, same time" because it is a race),

2. Whether either car has traveled any distance at all (if yes, then how far; if the slower car has traveled one lap, then the faster car has finished, and if no, then the answer is 60 mph),

3. What is the shape of the track (to Alanjai's point, a regular track requires offset starting positions, whereas a figure-8 track with fixed lanes would not), and finally

4. Why the question is worded so poorly ("to finish at the same car to finish at the same time" ... I mean, come on, that's practically not even literate).

Speed

a = Car A speed = 60 mph

b = Car B speed = 30 mph

t = Time Elapsed (in hours)

d = Race Distance (in miles)

((t * a) = distance traveled by Car A) - d = Distance Remaining Car A = dra

((t * b) = distance traveled by Car B) - d = Distance Remaining Car B = drb

x= mph that Car B has to drive for the remainder of the race

(drb/dra)= y

y * a = x

or

((t*b)-d))/((t*a)-d)) = y

y * a = x

Example:

t = 1 hour

d = 240 miles

((1 * 60) - 240 = 180 [distance remaining Car A]

((1 * 30) - 240 = 210 [distance remaining Car B]

210/180 = 1.666666667

1.666666667 * 60mph = 70 mph, the speed that Car B has to drive for the remainder of the race.

oh, yeah... in case you couldn't guess, I'm a Digg user.

oh, yeah... in case you couldn't guess, I'm a Digg user.

I agree with wildfire. This question is not grammatical and is unsolvable as written. The point seems to be that you should read the entire question (review the entire problem) before jumping in to solve the question that is immediately apparent. So, attention to detail is important at this company.

Assuming the question was mistyped into this discussion, and they want to know how fast the second car would have to go to finish at the same time as the first car, then the answer is: infinitely fast.

The question is better expressed as:

A car is driving a sixty-mile path at thirty miles per hour. At the half-way point, the driver wants to speed up so his average speed at the end of the path is sixty miles an hour. How fast does he have to go?

At the half-way point (30 miles) he has taken one hour for his drive. To average 60 MPH, he would have had one hour for the entire road. Therefore he has no time left, and must travel infinitely fast (for zero time) to average 60 MPH.

It doesn't matter what answer you give, it is how you come to your conclusion that counts here. There is missing information on purpose because they want to see how you solve problems, not if you can solve problems quickly. The cars, the track the speed doesn't matter, it is the questions you ask and the information gathering that counts.

Since there are only 2 cars in the race, the race is over and the instant one of the cars passes the finish line. One car finishes first, the other finishes second by default. The answer is that it doesn't matter how fast either of them are going, or how long the track is. They will always finish at the same time (not to be confused with "finishing with the same lap time").

I agree with SteveC. Once the either car finishes, the race is over.

The question was clearly misworded. If not, most of you would have failed.

The best answers here are from toolbelt_1 and dadag. Morgan Stanley needs people with exceptionally strong quantitative abilities and communication skills. The interviewer gives you a vaguely worded question to see (1) how you would gather the rest of the information and (2) how you would use it. In the course of a real workday your manager, client or other stakeholder will rarely provide a perfectly well-defined request for information. In the heat of the moment, important questions are worded quickly and vaguely, yet your performance will be judged based on how well you respond. One of your most crucial job skills is determining true requirements through timely and effective follow-up communication, intuition and experience.

Both cars will finish at the same time if the track length was 0.

This is typical of Morgan Stanley. Search a bit more and read about the lack of communication and clarity within this company--and when the result is as it should be (wasted time and effort) they blame the lower level worker as Al did above. If you ask for more information, you get more of the same -- confusion. Al might ALSO work for Morgan Stanley and makes a flimsy excuse for wasted time in having to track down pertinent information for the task. He makes no mention of the increasing frustration, lost productivity and the poor underlings that take the blame for poor managers. There are a few upper level managers who communicate and instruct their reports very well. It is a breathe of fresh air. They will tell the report the objective, quick background and the task and then you go do it. That simple. Others have more time for backstabbing, gossip and slimy character demonstrations than instructing their reports. No wonder they will never catch up to Goldman Sachs. They just don't get it.

it's quite easy guys, just think:

30 mph is the current speed

x is the race lenght

60 mph is the target average speed

so theanswer is

30*(miles raced/ total race) + speed to achieve*(iles missing/tot. race) = 60

speed = i know that yu can dothis.....;)

I'm pretty sure this is how the question is supposed to be worded which makes Mike's response correct. If two cars are traveling in a two lap race on any length track, one going 60mph for the entire race and one going 30mph to begin the race, how fast must the slower car travel for the rest of the race once the faster car finishes its first lap to finish at the same time as the faster car?

If this is the case then we can do the following.

distance = rate X time

let d = the length of the track.

After the fast car completes one lap the slow car will have completed one half lap, or .5d

So the fast car has d left to go and the slow car has 1.5d left to go.

since distance = rate x time, and the fast car is going at 60mph, we have d = 60t where t is time.

For the slow car, if we let x be the rate it will go (so what we're ultimately trying to solve for, we have 1.5d = xt.

now substituting d = 60t in we have 1.5 x (60t) = xt

Since the track has some distance, t cannot be zero so we can divide t out leaving 1.5 x 60 = x = 90mph. Hence the slow car would have to travel 90mph the second lap to finish at the same time as the fast car.

Make it simple, it depend on the fast car, if fast car got no problem( like break down , flat tires...), it hard to pass. The slow car just got to wait, time and opportunity is the key.

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It's impossible, the faster car will be done the race by the time the slower car finishes the first lap.