Solution: The time taken by both Eitan and Dmitri to reach each other is 1 hour 15 minutes and they are 68.75 miles away from the city.
Explanation:
Let the time taken by both Eitan and Dmitri to reach each other be t.
It is given that the speed of Eitan's train is 65 miles per hour and the speed of Dmitri's train is 55 miles per hour. The total distance between both Eitan and Dmitri is 150 miles.
[tex]65t+55t=150[/tex]
[tex]120t=150[/tex]
[tex]t=\frac{150}{120}[/tex]
[tex]t=1\frac{1}{4}[/tex] hours
Since we know that 1 hour = 60 min, therefore [tex]\frac{1}{4} hour=\frac{1}{4}(60) min[/tex]
[tex]\frac{1}{4} hour=15min[/tex]
Hence the time taken by both Eitan and Dmitri to reach each other is 1 hour 15 minutes.
The Dmitri's train starts from the city and travelling away from the city. The distance covered by second train in 1 hour 15 minutes is equal the distance outside the city will they be met.
In one hour second train cover 55 miles and in 15 minutes it will cover [tex]\frac{55\times15}{60} =\frac{55}{4} =13.75[/tex].
So the total distance covered by the Dmitri's train in 1 hour 15 minutes is [tex]55+13.75=68.75[/tex].
Therefore they are 68.75 miles away from the city.
