Question

Eitan is on a train heading west into the city while Dmitri is on a train on the adjacent track heading east, away from the city. They start 150 miles apart. Eitan’s train is traveling at an average speed of 65 miles per hour while the average speed of Dmitri's train is 55 miles per hour. How long will it take the two trains to reach each other? How far outside the city will they be?

Answer 1

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.

$65t+55t=150$

$120t=150$

$t=\frac{150}{120}$

$t=1\frac{1}{4}$ hours

Since we know that 1 hour = 60 min, therefore $\frac{1}{4} hour=\frac{1}{4}(60) min$

$\frac{1}{4} hour=15min$

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 $\frac{55\times15}{60} =\frac{55}{4} =13.75$.

So the total distance covered by the Dmitri's train in 1 hour 15 minutes is $55+13.75=68.75$.

Therefore they are 68.75 miles away from the city.

Answer 2

The time when the two trains reach each other is 1.25 hours
The trains are 68.75 away from the city when they reach each other.