Part A
See the diagram below for the table.
Here's how to set up the table.
Let t be the time it takes to make the return trip.
15 min = (15 min)*(1 hr/60min)
15 min = (15/60) hr
15 min = 1/4 hr
Since the cheetah traveled 15 minutes total, this means it traveled 1/4 of an hour total.
If it took t hours to go back home then it took 1/4 - t hours to get to the river. The values in the time column must add up to 1/4 hour.
The speeds given to us are placed in the table as is.
Multiply those speeds with the time expressions to get the distance expressions.
For the first distance we get
d = r*t
d = 40*(1/4-t)
d = 40*(1/4)+40*(-t)
d = 10-40t
Representing the distance traveled going from home to the river.
The second distance equation is
d = r*t
d = 70*t
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Part B
The equation is 10-40t = 70t
Simply set each distance equal to one another. This works because the cheetah travels the same distance from home to the river, and then back again.
In other words,
distance from home to river = distance from river to home
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Part C
Let's solve the equation formed in part B
10-40t = 70t
10-40t+40t = 70t+40t .... adding 40t to both sides
10 = 110t
110t = 10
110t/110 = 10/110 .... dividing both sides by 110
t = 1/11 hours
t = 60/11 minutes .... multiply by 60 to convert from hrs to min
t = 3600/11 seconds ... multiply by 60 to convert from min to sec
So,
3600/11 sec = 327.2727 sec
3600/11 sec = (300 sec) + (27.2727 sec)
3600/11 sec = (300/60) min + (27.2727 sec)
3600/11 sec = 5 min + 27.2727 sec
3600/11 sec = 5 min, 27.2727 sec
Answer: Approximately 5 min, 27.2727 sec
