Two trains leave the station at the same time, one heading west and the other east. the westbound train travels 20 miles per hour faster than the eastbound train. if the two trains are 800 miles apart after 5 hours, what is the rate of the westbound train?

Givens

W = E + 20

d = 800 miles

d1 = Westbound train.

d2 = Eastbound train.

t = 5 hours.

Equations

West bound

W*5 = d1 miles

d1 = W*5

East bound

E*5 = (800 - d1)

Step One

Substitute d1 into the Eastbound train.

E*5 = (800 - 5*W)

Step Two

Substitute E = W + 20 on the left side of the above equation.

(W + 20)5 = 800 - 5W

Step Three

Solve Remove the brackets

5W + 100 = 800 - 5W Add 5W to both sides.

10W + 100 = 800 Subtract 100 from both sides.

10W = 800 - 100

10W = 700

W = 700/10

W = 70

E = W + 20

E = 70 + 10 = 90

Check

70*5 = 350

90*5 = 450

Total distance = 800

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

i saw this question before, dont know the asnwer srry

step-by-step explanation: