SOLUTION: A boy cycles x km at 8 km/hr and y km at 20 km/hr . His total time is 3.5 hours. The total time taken to the cycle (2x+4) km at 8 km/hr and y/3 km at 20 km/hr is 5 hours. Find x a

Algebra ->  Linear-equations -> SOLUTION: A boy cycles x km at 8 km/hr and y km at 20 km/hr . His total time is 3.5 hours. The total time taken to the cycle (2x+4) km at 8 km/hr and y/3 km at 20 km/hr is 5 hours. Find x a      Log On


   



Question 1043319: A boy cycles x km at 8 km/hr and y km at 20 km/hr . His total time is 3.5 hours. The total time taken to the cycle (2x+4) km at 8 km/hr and y/3 km at 20 km/hr is 5 hours. Find x and y
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x km at 8 km/hr and y km at 20 km/hr . His total time is 3.5 hours.
          RATE          TIME         DISTANCE
SLOW       8                          x
FAST       20                         y
Total                   3.5


Fill the missing cells and see what might be done if anything from that.
          RATE          TIME         DISTANCE
SLOW       8            x%2F8              x
FAST       20           y%2F20              y
Total                   3.5

The obvious equation is x%2F8%2By%2F20=3.5.
-
Simplify this equation.
40%28x%2F8%29%2B40%28y%2F20%29=40%283.5%29
5x%2B2y=140



The "total" time taken to the cycle (2x+4) km at 8 km/hr and y/3 km at 20 km/hr is 5 hours.
That is saying 5 hours is "total time"; and then ..... this is a different description, going like this:
?          8                         2x+4
?         20                          y/3
total                  5

to be filled this way:
         RATE        TIME                 DISTANCE
?          8        %282x%2B4%29%2F8              2x+4
?         20        %28y%2F3%29%2F20              y%2F3
total                  5

The only obvious equation for this part of the description is
%282x%2B4%29%2F8%2By%2F%283%2A20%29=5
simplifiable to
%282x%2B4%29%2F8%2By%2F60=5

15%282x%2B4%29%2B2y=600
30x%2B60%2B2y=600
15x%2B30%2By=300
15x%2By=270

The two equations found as a system are this one:
highlight%28system%285x%2B2y=140%2C15x%2By=270%29%29
Solve this system.
-
(This would give x=16.)



---
scratch work
2*2*2, 2*2*3*5
2*2*2*3*5 LCD