A passenger train traveled 120 miles in the same amount of time it took a freight train to travel 70 miles. The rate of the freight train was 30 miles per hour slower than the rate oft the passenger train. Find the rate of the passenger train.

Rate of passenger train is 42 mph

Step-by-step explanation:

Let the rate of the passenger train be x

Mathematically;

time = distance/speed

We have the time equal in this case

Rate of freight train is 30 mph slower

So if the rate of passenger train is x mph, rate of freight will be x + 30 mph

Thus, mathematically, we have ;

120/x + 30 = 70/x

70(x + 30) = 120 * x

70x + 2100 = 120x

120x-70x = 2100

50x = 2100

x = 2100/50

x = 42 mph

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

ruth is 6 years old

step-by-step explanation:

6 + 24 = 30,   so 6/30 = .2  

if you do 1/5 it also equals .2, so that is the answer.