SOLUTION: Hi, this problem's been bugging me for a few days now... Thanks for the help! Two bicyclists are 7/8 of the way through a mile long tunnel when a train approaches the closer end

Question 1040624: Hi, this problem's been bugging me for a few days now... Thanks for the help!
Two bicyclists are 7/8 of the way through a mile long tunnel when a train approaches the closer end at 40 mph. The riders take off at the same speed in opposite directions and each escapes the tunnel as the train passes them. How fast did they ride?
Thanks again!
Found 3 solutions by Boreal, ikleyn, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
I am assuming the riders did 7/8 of a mile in the same time that the train did a mile.
A train at 40 mph does a mile in 90 seconds.
The riders do 7/8 mile in 90 seconds.
in 40 times 90 seconds (3600 seconds), the riders have ridden for an hour.
40 * (7/8)=35 mph.
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
Hi, this problem's been bugging me for a few days now... Thanks for the help!
Two bicyclists are 7/8 of the way through a mile long tunnel when a train approaches the closer end at 40 mph.
The riders take off at the same speed in opposite directions and each escapes the tunnel as the train passes them.
How fast did they ride?
Thanks again!
~~~~~~~~~~~~~~~~~~~~~~~~~~

It is a classic problem on Travel and Distance known for many years. (And I know it very well . . . ) The similar problem was solved in the lesson A man crossing a bridge and a train coming from behind in this site. I even copy and past that problem condition here for your convenience. A man is three eighths of the way across a bridge when he hears a train coming from behind. If he runs as fast as possible back toward the train, he will get off the bridge just in time to avoid a collision. Also, if he runs as fast as possible away from the train, he will get off the bridge (on the other side) just in time to avoid a collision. The train is traveling at 60 miles per hour. How fast does the man run? You can consider and use that solution as a sample for your problem. If you still will have difficulties in solving it, then please let me know (through the "Thank you" message . . ), and I will help you. In this case please do not forget to refer on the problem ID number (1040624) in order I could identify it. Thank you.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Hi, this problem's been bugging me for a few days now... Thanks for the help!
Two bicyclists are 7/8 of the way through a mile long tunnel when a train approaches the closer end at 40 mph. The riders take off at the same speed in opposite directions and each escapes the tunnel as the train passes them. How fast did they ride?
Thanks again!

I'll give you some hints.
By the time the train entered the tunnel, the shorter-journey cyclist was out, and the longer-journey cyclist had traveled , which means that he/she had
to travel to get out of the tunnel before the train exited. Now, the time the train took to travel through the tunnel was the same time that the
longer-journey cyclist took to exit the tunnel. Now, can you put 2 and 2 together to find the speed, which was also the shorter-journey cyclist's speed?
By the way, the speed was NOT 35 mph
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