SOLUTION TO LAST MONTH'S QUIZ
1. 32 mph
2. 22.5 mph or 50 mph
3. 01:36 pm.
Notes
1. The position of the hiker divides the length of the tunnel
internally in the ratio 3:5. So the position of the train
divides the length of the tunnel externally in the ratio 3:5.
So the train is 1.5 tunnel lengths from the tunnel entrance
(and 2.5 lengths from the exit). So train travels 1.5 lengths
while hiker travels 3/8 lengths, etc.
2. Total length of two trains = 210 + 120 = 330 m
So total time to pass each other = 330/(60 + v)
In this time A moves either 180 or 240 m.
So 60 X 330/(60 + v) = 180 or 240
Solving, v = 22.5 or 50.
3. Impose a Southerly velocity of 2.25 mph on the whole system.
Then Andy is reduced to rest, and Betty's velocity becomes as
shown. Note that 2.25:3 = 3:4, so the triangle of velocities
is a 3:4:5 triangle, and Betty's velocity is 3.75. Closest
approach is at X, and triangle SMX also is 3:4:5. So
MX = 6 ml. and time = 6/3.75 = 1.6 hr.
