A herd of elephants on the savannah is moving in a straight line at $4$ kilometers per hour, headed directly toward a biologist who has been tracking them. Meanwhile, the biologist is also driving toward them at $69$ kilometers per hour. If they started out $14$ kilometers apart, how long will it be before they encounter one another? $\newline$ If necessary, round your answer to the nearest minute. $\newline$ hours and minutes

Full solution

Q. A herd of elephants on the savannah is moving in a straight line at

4

kilometers per hour, headed directly toward a biologist who has been tracking them. Meanwhile, the biologist is also driving toward them at

69

kilometers per hour. If they started out

14

kilometers apart, how long will it be before they encounter one another?

\newline

If necessary, round your answer to the nearest minute.

\newline

____ hours and ____ minutes

Calculate Combined Speed: First, we need to determine the combined speed at which the herd of elephants and the biologist are moving towards each other. $\newline$ Speed of elephants: $4$ kilometers per hour $\newline$ Speed of biologist: $69$ kilometers per hour $\newline$ Combined speed $=$ Speed of elephants $+$ Speed of biologist $\newline$ Combined speed $= 4 \, \text{km/h} + 69 \, \text{km/h}$ $\newline$ Combined speed $= 73 \, \text{km/h}$
Determine Encounter Time: Next, we calculate the time it will take for the biologist to encounter the herd of elephants. We know the distance between them is $14$ kilometers, and we have just calculated their combined speed to be $73$ kilometers per hour. $\newline$ Time $=$ Distance $/$ Combined speed $\newline$ Time $=$ $14$ km $/$ $73$ km/h $\newline$ Time $hickapprox$ $0.1918$ hours
Convert Time to Minutes: Now, we need to convert the time from hours to minutes. Since there are $60$ minutes in an hour, we will multiply the decimal part of the hour by $60$ . $\newline$ Minutes = $0.1918$ hours $\times 60$ minutes/hour $\newline$ Minutes $\approx 11.508$ minutes $\newline$ Since we need to round to the nearest minute, we round $11.508$ to $12$ minutes.
Express Time in Hours and Minutes: Finally, we express the time before the biologist and the herd of elephants meet in terms of hours and minutes. From our previous calculation, we have $0$ hours and approximately $12$ minutes.