Answer :
228 km is the distance (in kilometres) between City2 and City1.
Let's denote the distance traveled by Train E as [tex]d_E[/tex] and the distance traveled by Train F as [tex]d_F[/tex].
- According to the problem, Train F has traveled 18 km more than Train E when they meet. Hence, we can write:
[tex]d_F = d_E + 18 km[/tex]
- Since both trains start at the same time and meet each other, they have traveled for the same amount of time, which we can denote as t. Using the formula for distance (distance = speed × time), we can express the distances in terms of their speeds and time:
[tex]d_E = 70 \, \text{km/h} \times t[/tex]
[tex]d_F = 82 \, \text{km/h} \times t[/tex]
- Substituting the expression for [tex]d_F[/tex] from the above equation into the first equation:
82 × t = 70 × t + 18
- Solving for t:
82t - 70t = 18
12t = 18
t = 18 / 12
t = 1.5 hours
- Now, we can find the distance traveled by each train:
[tex]d_E = 70 \times 1.5 = 105 \, \text{km}[/tex]
[tex]d_F = 82 \times 1.5 = 123 \, \text{km}[/tex]
- Finally, the total distance between City1 and City2 is the sum of the distances traveled by both trains:
Total distance = [tex]d_E + d_F = 105 \, \text{km} + 123 \, \text{km} = 228 \, \text{km}[/tex]
