Two passenger trains 200 miles apart are headed toward each other on the same track—one at 50 mph and the other at 80 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?

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Two passenger trains 200 miles apart are headed toward each other on the same track—one at 50 mph and the other at 80 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?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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The closing speed of the trains is 50 + 80 = 130 mph. The distance traveled at the closing speed is 200 miles, therefore the time to collision is t = 200/130 hr. Ironman flies for 200/130 hr at 150 mph, therefore the distance flown is: \[\large \frac{200}{130}\times\frac{150}{1}=(you\ can\ calculate)\ miles\]
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