Problema Solution
Two train engines are approaching each other on the same track. They begin at a distance of 20 miles, and are each traveling at a rate of 10 mph. At the instant they begin, a dragonfly takes off from the front of one train at a rate of 15mph. When it meets the front of the other train, it immediately turns around and heads back towards the first train. It continues back and forth until it is crushed when the two trains meet.
What is the total distance traveled by the fly on its zig-zag journey before it meets its end?
Answer provided by our tutors
let 't' denotes the time
The fly reaches the second train when:
15t = 20 - 10t
by solving we find:
t1 = 4/5 s
click here to see the step by step solution of the equation:
for t1 = 4/5 at which point it has traveled a distance d1 = 15*t1= 15(4/5) = 12 mi.
It then turns around and reaches the first train again when
12 - 15t = 10(4/5) + 10t
by solving we find:
t2 = 4/25 s
click here to see the step by step solution of the equation:
Continuing, the total distance traveled by the fly is given by summing the series:
15(4/5 + 4/5^2 + 4/5^3....)=15*1 = 15 mi
click here to see the sum of the series: sum 4/5^n, n=1 to infinity
https://www.wolframalpha.com/input/?i=sum+4%2F5^n%2C+n%3D1+to+infinity
he total distance traveled by the fly on its zig-zag journey before it meets its end is 15 miles.