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Question 1069779: sally left point A at 6 am and reached point B at 10 am. Jane left one hour later and arrived at point B at the same time as sally. Jane traveled two miles an hour faster than sally.
Which equation can be used to find the missing information?
A. (Rs)(4)=(Rs-2)(3)
B. (Rs)(4)=(Rs)(3)
C. (Rs)(4)=(Rs+2)(3)
D. (Rj)(4)=(Rj+2)(3)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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