Question 1201539
upstreatm, the boat is traveling against the current.
downstream, the boat is traveling with the current.


your equations are:


12 * (R - 4) = D + 30
8 * (R + 4) = D
simplify to get:
12 * R - 48 = D + 30
8 * R + 32 = D
subtract 30 from both sides of the first equqtion and leave the second equation as is to get:
12 * R - 78 = D
8 * R + 32 = D
since both equation are equal to D, you can set them equal to each other to get:
12 * R - 78 = 8 * R + 32
add 78 to both sides of the equation and subtract 8 * R from both sides of the equastion to get:
4 * R = 110
solve for R to get:
R = 110 / 4 = 27.5
replace R with that in your two original equations to get:
12 * R - 78 = D becomes 12 * 27.5 - 78 = 252
8 * R + 32 = D becomes 8 * 27.5 + 32 = 252
it appears that R = 27.5 is good and that D = 252 is also good.
you are asked to find how long it takes the boat to travel D - 64 kilometers upstream.
upstream, the boat is traveling against the current, therefore (R - 4) * T = D - 64
since R is 27.5 and D is 252, the equation becomes 23.5 * T = 188.
solve for T to get:
T = 188 / 23.5 = 8
it takes the boat 8 hours to travel 188 kilometers upstream.
that's your solution.