Two buses go from sacramento to san diego. the express bus makes the trip in 6.8 hours and the local bus takes 10.2 hours for the trip. the speed of the express bus is 25 mph faster than the speed of the local bus. find the speed of both buses.

Speed of local bus is 50 mph  and speed of express bus is 75 mph

Step-by-step explanation:

let say speed of local bus = x

so speed of express bus = x + 25

Distance = Speed × Time

Distance traveled by local bus  = x × 10.2 = 10.2x

Distance traveled by express bus = (x + 25) × 6.8

since Distance traveled by local bus is same as Distance traveled by express bus

⇒10.2x = (x + 25) × 6.8

⇒ 10.2x = 6.8x + 170

⇒ 10.2x - 6.8x = 170

⇒ x = 170/3.4 = 50

So Speed of local bus = x = 50 mph

and Speed of express bus =  x + 25 = 50 + 25 = 75 mph

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.