Two freight trains leave the station in Allenville at the same time. The first train is headed due south at a speed of $43$ kilometers per hour. In comparison, the second train is going due north at $64$ kilometers per hour. In how long will the trains be $450$ kilometers apart? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes

Full solution

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

43

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

64

kilometers per hour. In how long will the trains be

450

kilometers apart?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

Calculate Combined Speed: Calculate the combined speed of the two trains moving in opposite directions. $\newline$ Speed of first train: $43$ kilometers per hour $\newline$ Speed of second train: $64$ kilometers per hour $\newline$ Combined speed = Speed of first train + Speed of second train $\newline$ Combined speed = $43 + 64$ $\newline$ Combined speed = $107$ kilometers per hour
Calculate Time Apart: Calculate the time it takes for the trains to be $450$ kilometers apart using the combined speed. $\newline$ Distance to be apart = $450$ kilometers $\newline$ Combined speed = $107$ kilometers per hour $\newline$ Time = Distance / Speed $\newline$ Time = $450 / 107$ $\newline$ Time $\approx 4.2056074766$ hours
Convert Decimal to Minutes: Convert the decimal part of the hours into minutes. $\newline$ Decimal part of hours $\approx 0.2056074766$ $\newline$ Minutes = Decimal part of hours $\times 60$ $\newline$ Minutes $\approx 0.2056074766 \times 60$ $\newline$ Minutes $\approx 12.3364486$ $\newline$ Round to the nearest minute: $12$ minutes
Combine Hours and Minutes: Combine the whole number of hours and the rounded minutes to get the final answer. $\newline$ Hours = $4$ $\newline$ Minutes = $12$ $\newline$ So, it will take approximately $4$ hours and $12$ minutes for the two trains to be $450$ kilometers apart.