A car and a bus set out at 2pm from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car.

the speed of the car is 50 mph

Step-by-step explanation:

Let x represent the speed of the bus. The average speed of the car is 30 mph slower than twice the speed of the bus. It means that the speed of the car is (2x - 30) mph.

The car and the bus set out at 2pm from the same point, headed in the same direction.

Distance = speed × time

In two hours, It means the distance covered by the bus is

2 × x = 2x

In two hours, the car is 20 miles ahead of the bus. It means that the distance covered by the car in 2 hours is (2x + 20) miles

Time = distance/speed

Therefore,

2 = (2x + 20)/(2x - 30)

Cross multiplying, it becomes

2(2x - 30) = 2x + 20

4x - 60 = 2x + 20

4x - 2x = 20 + 60

2x = 80

x = 80/2

x = 40 mph

Speed of the car is

2x - 30 = 2 × 40 - 30 = 50 mph

b. x + 1

step-by-step explanation:

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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.