SOLUTION: The distance to Arsh’s cottage is 230km. Part of the trip is spent driving on a paved road where the limit is 80km/h. The rest of the trip is spent driving on gravel road with th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The distance to Arsh’s cottage is 230km. Part of the trip is spent driving on a paved road where the limit is 80km/h. The rest of the trip is spent driving on gravel road with th      Log On


   

Question 1021980: The distance to Arsh’s cottage is 230km. Part of the trip is spent driving on a paved road where the limit is 80km/h. The rest of the trip is spent driving on gravel road with the limit being 50km/h. If the trip takes 4 hours, how many hours are spent on each part?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
                     rate        time       distance

PAVED                 80

GRAVEL                50

Total                            4            230

Basic uniform travel rates rule is RT=D to relate rate, time, and distance. Either pick variables for time OR variables for the distances, and fill-in the rest of the numbers for the data table. Make the equations and solve the system.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

The distance to Arsh’s cottage is 230km. Part of the trip is spent driving on a paved road where the limit is 80km/h. The rest of the trip is spent driving on gravel road with the limit being 50km/h. If the trip takes 4 hours, how many hours are spent on each part?
Let time spent on paved road, be T

Then time spent on gravel road = 4 – T

We then get the following DISTANCE equation: 80T + 50(4 – T) = 230

80T + 200 – 50T = 230

80T – 50T = 230 – 200

30T = 30

T, or time spent on paved road = 30%2F30, or highlight_green%28matrix%281%2C2%2C+1%2C+hour%29%29

Time spent on gravel road: 4 – 1, or highlight_green%28matrix%281%2C2%2C+3%2C+hours%29%29