Iron Man MPH Speed

Question

Two passenger trains 200 miles apart are headed toward each other on the same track—one at 50 mph and the other at 70 mph. Ironman responds to the danger by flying back and forth between the trains, hoping to stop them before disaster strikes. Unfortunately, when he reaches each train, an invisible force repulses him back, jolting him in the opposite direction (toward the other train). If Ironman maintains a constant speed of 150 mph the entire time—while flying back and forth between the trains—how far will he have flown when the trains collide?

Answer 1

v₁ = relative velocity of the trains to each other = (50+70) mph = 120 mph

 

d = initial distance between trains = 200 mi

 

v = Ironman speed = 150 mph (I assume it is relative to the ground)

 

t = time until trains collide 

 

t = d / v₁ = 200 / 120 hrs = 1.67 hours

 

Total flying time for Ironman = time until trains collide = t

 

d₁ = total distance flown by Ironman before the trains collide

 

d₁ = vt = (150 mph) (1.67 hours) ≅ 251 miles

 

Modification:  If no rounding off is used, then t = 200/120 hrs

 

d₁ = vt = (150)(200/120) miles = 250 miles exact

Answer 2

This is a modification of the "fly and two trains" problem (been around since I was in HS in the 60's!)

First consider the trains. They are covering the distance at 120 mph (50 + 70). So they meet after 5/3 hour (200 / 120)

Now the Iron Man is flying the same amount of time.

150 mph · 5/3 hour = 250 miles

 

Now consider that Iron Man shall be squished by the trains at 100 minutes. He has to "pull up" short of that time.