SOLUTION: it is a 230 km trip. part of the trip is on gravel roads where you can only travel 50km per hour and part is on paved roads where you can travel 80km per hour. if the total trip ta

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Question 1102358: it is a 230 km trip. part of the trip is on gravel roads where you can only travel 50km per hour and part is on paved roads where you can travel 80km per hour. if the total trip takes 4 hours, how far do they travel on paved roads and how far do they travel on gravel roads?

Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
            SPEEDS     TIMES          DISTANCES
GRAVEL       50        d/50             d
PAVED        80        (230-d)/80     230-d
Total                   4             230

highlight_green%28d%2F50%2B%28230-d%29%2F80=4%29
Solve for d and evaluate 230-d.

useful first step, multiply by 10.
d%2F5%2B%28230-d%29%2F8=40

useful second step, unless combined in first step, multiply both sides by 5%2A8.
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highlight_green%288d%2B5%28230-d%29=1600%29
.
.
.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=4
x=4-y
50*x+80*y=230
50*(4-y)+80*y=230
50*4-50y+80*y=230
200-50y+80*y=230
200+(80-50)*y=230
200+30*y=230
30*y=230-200
30*y=30
y=1
x+y=4
x+1=4
x=3
150 km at 50 kph for 3 hr on gravel
80 km at 80 kph for 1 hr on paved roads
check
50*3+80*1=230
150+80=230
230=230
if 230=230 all is well
all is well