SOLUTION: 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 sall

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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