A freight train leaves centralia for Chicago at the same time a passenger train leave Chicago for centralia. The freight train travels at the speed of 45 mph in the passenger train travels at a speed of 64 mph. If Chicago in centralia are 218 miles apart, how long will it take for the trains to meet?

It will take 2 hours for the trains to meet

Step-by-step explanation:

When two objects move towards each other and started at the same time the distance between the two starting points is the sum of the distance that each one moves until meet each other

The formula of the distance is Distance = Speed × Time

A freight train leaves Centralia for Chicago

A passenger train leave Chicago for Centralia

They started at the same time

The distance between Centralia and Chicago = distance of freight train + distance of passenger train ⇒ when they meet each other

∵ The freight train travels at the speed of 45 mph

∴ Its speed is 45 miles per hour

∵ The passenger train travels at a speed of 64 mph

∴ Its speed is 64 miles per hour

- Assume that they will meet each other after t hours

∴ The distance of the freight train = 45 × t = 45 t miles

∴ The distance of the passenger train = 64 × t = 64 t miles

∵ Chicago and Centralia are 218 miles apart

- That means add the distance of the two trains and equate the

    sum by 218

∴ 45 t + 64 t = 218

∴ 109 t = 218

- Divide both sides by 2

∴ t = 2

∵ t represents the time that they will take to meet each other

∴ The two trains will meet each other after 2 hours

∴ It will take 2 hours for the trains to meet