Two freight trains leave the station in Lexington at the same time. The first train is headed due south at a speed of $22$ miles per hour. In comparison, the second train is going due north at $35$ miles per hour. In how long will the trains be $380$ miles apart? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

Full solution

Q. Two freight trains leave the station in Lexington at the same time. The first train is headed due south at a speed of

22

miles per hour. In comparison, the second train is going due north at

35

miles per hour. In how long will the trains be

380

miles apart?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

\newline

Find Combined Speed: We need to find the combined speed of the two trains moving in opposite directions. $\newline$ Speed of first train: $22$ miles per hour $\newline$ Speed of second train: $35$ miles per hour $\newline$ Combined speed = Speed of first train + Speed of second train $\newline$ Combined speed = $22 + 35$ $\newline$ Combined speed = $57$ miles per hour
Calculate Time: Now, we need to calculate the time it takes for the trains to be $380$ miles apart using their combined speed. $\newline$ Time $=$ Distance $/$ Speed $\newline$ Time $=$ $380$ miles $/$ $57$ miles per hour $\newline$ Time $hickapprox 6.6667$ hours
Separate Hours and Minutes: To find the time in hours and minutes, we need to separate the decimal part from the whole number. $\newline$ The whole number is $6$ hours. $\newline$ To find the minutes, we multiply the decimal part by $60$ . $\newline$ Minutes = $0.6667 \times 60$ $\newline$ Minutes $\approx 40$ minutes
Final Result: Therefore, the trains will be $380$ miles apart in $6$ hours and $40$ minutes.