ElectricPavlov

You are correct there ....and I can't solve them with my limited skills either !   

x + 3y = - 5

3y = -x -5

y = -1/3 x - 5/3        slope = - 1/3    parallel slope is the same  - 1/3

point slope form

(y-2) = - 1/3 ( x - -7)

y -2 =   - 1/3 x  - 7/3

y  = - 1/3 x  - 1/3               multiply by 3 to get rid of the fractions

3 y = -x -1     re-arrange

3y + x  = -1      now multiply by -3

- 9y - 3x = 3        take it from here  

Something is missing in your equations....there is no variable ! 

   I had my  COVID vaccine this morning and have been breathing paint fumes the rest of the day.....that's what I'm gonna use for an excuse !!!!!   Haha

               thanx Varxaax !

d / ( r  + e ) = 6         d / ( r- e ) = 30                 e = escalator speed      r = run speed

  30 r - 30 e = d

   6r + 6e = d      or          6e = d - 6r     <======  multiply by -5 and sub into top equation  

                            d = 30r-5d + 30 r

                          6d   = 60 r

                          60 / 6 = d/r = 10 seconds      Varaax is correct ......I fell prey to my warning about time in distance calcs !
 

Will check....thanx  V

This is kinda like the boat and current speed questions

(6 + 30)/ 2 = speed on still escalator = 18 seconds

Each triangle is 7.5*16=120    <======= slight mistake here Varxaax       We all have hiccups!

Base is   13 x 13 = 169 ft ^2

each of the triangles   is   1/2 b h =  1/2  13 x 16 = 104 ft²      there is 4 of them    104 *4 = 416 ft²

416 + 169 =  585 ft²

He needs to average   10 km / hour   (his goal)   

   he has run 2 km  @ 12 km/ hr       2km / 12 km/hr = 1 / 6  hr   (10 minutes)

          he has to run the remaining   8 km   in 50 minutes   (5/6 hr)       8 km/ (5/6 hr ) =  48/5  km/ hr     =  9.6   km / hr