Two buses are scheduled to arrive at the Middletown Bus Terminal at the same time. One bus is south of the terminal, driving north at $26$ miles per hour. At the same time, another bus is north of the terminal and is driving south at $59$ miles per hour. They are currently $70$ miles apart. How long will it be before the buses arrive at the terminal? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes $\newline$

Full solution

Q. Two buses are scheduled to arrive at the Middletown Bus Terminal at the same time. One bus is south of the terminal, driving north at

26

miles per hour. At the same time, another bus is north of the terminal and is driving south at

59

miles per hour. They are currently

70

miles apart. How long will it be before the buses arrive at the terminal?

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If necessary, round your answer to the nearest minute.

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____ hours and ____ minutes

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Calculate Combined Speed: We have: $\newline$ Speed of Bus $1$ : $26$ miles per hour (driving north) $\newline$ Speed of Bus $2$ : $59$ miles per hour (driving south) $\newline$ Distance apart: $70$ miles $\newline$ Find the combined speed of both buses. $\newline$ Speed of Bus $1$ + Speed of Bus $2$ = Combined speed $\newline$ $26 + 59 = 85$ $\newline$ Combined speed: $85$ miles per hour
Find Time Taken: With the combined speed of $85$ miles per hour, identify the time taken by both buses to cover the $70$ miles. $\newline$ Time $=$ Distance $/$ Combined speed $\newline$ Time $=$ $70$ $/$ $85$ $\newline$ Time $hickapprox$ $0.8235$ hours
Convert to Minutes: Convert the time taken from hours to minutes. $\newline$ $0.8235$ hours $\times 60$ minutes/hour $\approx 49.41$ minutes $\newline$ Since we need to round to the nearest minute, we get approximately $49$ minutes.
Identify Hours and Minutes: Identify the number of hours and minutes. $\newline$ In $0.8235$ hours, the number of whole hours is $0$ . $\newline$ The remaining time is approximately $49$ minutes. $\newline$ So, it will be $0$ hours and $49$ minutes before the buses arrive at the terminal.