brainteaser

[Jules6]

A train was going from Aye to Bea, but an hour after staring the engine developed a fault, and the train had to continue at 60% of its former speed. The driver said that if the fault had occurred 50 miles further on the train would have arrived 40 minutes sooner. How far is it from Aye to Bea?

[DOB]

There appears to be something missing from this brainteaser because there is several answers as far as I can see. One solution is: 110 miles. The train first travels 50 miles at 50mph which takes 1 hour. Then it travels 60 miles at 30 mph (60% of 50 mph) which takes 2 hours. Total journey = 110 miles takes 3 hrs. If the train had continued originally for another 50 miles at top speed the time taken is as follows: 100 miles at 50 mph = 2 hrs. The remaining 10 miles would be at 30 mph which would take 20 mins. Total journey = 110 miles takes 2 hrs 20 mins which is a saving of 40 mins. Solution 2: 350 miles. The train first travels 50 miles at 50mph which takes 1 hour. The it travels 300 miles at 30 mph (60% of 50 mph) which takes 10 hours. Total journey = 350 miles takes 11 hrs. If the train had continued originally for 50 miles at top speed the time taken is as follows: 100 miles at 50 mph = 2 hrs. The remaining 250 miles would be at 30 mph which would take 8 hrs 20 mins. Total journey = 350 miles takes 10 hrs 20 mins which is a saving of 40 mins. The same logic can be applied to any distance provided the train starts off at 50 mph.

[Shrek2]

I thought that some info missing also. I came up with 100 miles 50 miles at 50mph = 1hr. if still at full speed next 50 miles = 1hr = end of trip = total 2 hrs and 100 miles. compared to: 50 miles at 50mph = 1 hr. next 50 miles (speed reduced to 60% = 30mph) takes 1 hr 40mins = total of 2hrs 40 min and 100 miles = end of trip

[Dsg]

50mph is the right answer for the starting speed (it can be proved algebraically) but the distance between Aye and Bea is irrelevant because for the remainder of each alternative journey the "two" trains will be matching each other mile for mile !!

[bernardo]

Presumably the person who originally set the quiz didn't check it properly before asking Jules6.

[simplenomis]

Right. The train was originally doing 125 mph. This is because they would have done total distance - 50 /40mins -aaargh lost. Anycase, I got it to 125mph - so in first hous they covered 125miles - then in the second part they were travelling at 75mph - don't know for how long though!

[Jules6]

Hi, it seems there has been a mistake with this question and it is now void on my quiz sheet. Thanks to all who have been wracking their brains working it out. :-)