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?

the cyclists rode at 35 mph

Step-by-step explanation:

Assuming that the cyclists stopped, and accelerated instantaneously at the same speed than before but in opposite direction, then

distance = speed*time

since the cyclists and the train reaches the end of the tunnel at the same time and denoting L as the length of the tunnel:

time = distance covered by cyclists / speed of cyclists = distance covered by train / speed of the train

thus denoting v as the speed of the cyclists:

7/8*L / v = L / 40 mph

v = 7/8 * 40 mph = 35 mph

v = 35 mph

thus the cyclists rode at 35 mph