Train a and train b leave a central station at the same time they traveled at the same speed and in opposite directions with train a heading for station a and train b heading for station b train a reaches station after 4 hours and train b reaches the station after 3 1/2 hours. station a and station b are 562.5 miles apart. what is the rate of the trains?

Train a: 140.6 m/h

Train b: 160.7 m/h

Step-by-step explanation:

With problems involving distance, rate and time, you will use the formula:

d = rt where d = distance, r = rate and t = time

The distance is the same for both trains, 562.5 miles, however train a appears to be a bit slower and takes 4 hours to make the trip while train b makes the trip in 3.5 hours. Using the formula for each train:

train a: d = rt  

562.5 = r(4)

r = 140.6 miles/hour

train b: d = rt

562.5 = r(3.5)

r = 160.7 miles/hour

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.