I found the quiz on the National Museum of Mathematics website (www.MoMath.org) after it appeared in the WSJ.

Please let me know how you work the problem. I will post all correct answers or alternatively will send the solution privately to anyone who requests it if no one figures it out.

Two-Train Timing Quiz

How long does it take a 1.25-mile-long freight train going 30 miles an hour to pass a 0.25-mile-long passenger train going 60 miles an hour in the opposite direction, from the time that the engines first reach each other to the time that the last cars just clear each other?

Sorry could not complete quiz. At school was never good at these type questions

ReplyDeleteI had a friend help me with the quiz. Still don't get it. Help!!!

ReplyDeleteHi Doug!

ReplyDeleteHere's my stab at the Train Quiz.

Hope all is well with you.

Answer: 1 minute

Long Train : Length = 1.25 mi, speed = 30 mph

Short Train: Length = .25 mi, speed = 60 mph

This is equivalent to:

Long Train : Length = 1.25 mi, speed = 90 mph

Short Train: Length = .25 mi, speed = 0 mph (standing still)

The rear of the Long Train has to travel the length of both trains (1.25 + .25) = 1.5 mi

1.5 mi / 90 mph = 1 minute

Another way to look at it:

At start

Long Train (30mph): |---.25---|---.25---|---.25---|---.25---|---.25à|

Short Train (60 mph): |<--.25---|

After 1 minute

Long Train travels ½ mile: |---.25---|---.25---|---.25---|---.25---|---.25à|

Short Train travels 1 mile: |<--.25---|

Bullseye

DeleteAnother fun quiz - thanks!

DeleteDoug - My answer is 1 minute.

ReplyDeleteHow did you get it?

DeleteSince the trains are traveling in opposite direction to each other, the end speed is the combination of the two speeds., i.e. 60 + 30 = 90 m.p.h. = 90/60 = 1.5 m.p.min.

DeleteThe length of the trains are 1.25 miles + 0.25 miles = 1.5 miles and that is the length the two trains have to travel for last cars of the two freight trains to clear each other.

Therefore time taken to travel distance mentioned above is 1.5 m.p.min/1.5 m. = 1 min.

This one is hard..not sure i got it to be honest , but here is how i did it.

ReplyDeleteOne train is moving 60 MPH which is one mile per minute. The other train is 1 .25 miles long so...if the bigger train was not moving it would take 1.5 minutes to totally pass the larger train (1.25 miles plus the .25 miles of the other train). But the other train is also moving at 30 mph so we have to factor that in. This is where i get lost. I am guessing that at 30 MPH it would take the larger train 30 seconds to pass the other train.(30 mph equals 1/2 mile a minute and .25 miles in 30 seconds) So i would reduce the total time by 30 seconds and I come up with exactly one minute.

Will take a stab at it. If am right will show how.

ReplyDelete.166 minutes to pass each other.

You must be doing something right because 0.166 is correct but not in minutes. 0.166 minutes is less than 10 seconds so the trains would really be flying. Look again @ your units & I think you have it.

DeleteDoug,

ReplyDeleteSince the length of both trains is 1.5 miles & using the formula D = R * T to find T;

60 * T + 30 * T = 1.5

90 * T = 1.5

T = 1.5/90 = 1/60 = 1 minute to completely pass each other.