Question 1069779
rate * time = distance.


for sally, this equation becomes Rs * 4 = d
for jane, this equation becomes Rj * 3 = d


since they are both equal to d, then they are both equal to each other and you get:


Rs * 4 = Rj * 3.


you are given that jane travels 2 miles an hour faster than sally.


this means that Rj = Rs + 2.


Rs * 4 = Rj * 3 becomes Rs * 4 = (Rs + 2) * 3


that would be selection C.


we would solve for Rs as follows:


start with Rs * 4 = (Rs + 2) * 3
simplify to get Rs * 4 = Rs * 3 + 6
solve for Rs to get Rs = 6.


since Rj is 2 miles per hour faster, then Rj = 8.


since you know the two rates, you can now calculate the distance.


Rs * 4 = d becomes 6 * 4 = d which gets you d = 24 miles.


Rj * 3 = d becomes 8 * 3 = d which gets you d = 24 miles.


the distance is 24 miles.


it takes sally 4 hours to travel that distance at 6 miles per hour.


it takes jane 3 hours to travel that distance at 8 miles per hour.


8 miles an hour is 2 miles an hour faster than 6 miles an hour.


Rj = Rs + 2 was the correct way to determine jane's rate.


once you knew that, the substitution allowed you to solve for Rs which then allowed you to solve for Rj.