I have two word problems I can't figure out.?

Question

1) Two cars leave Chicago at the same time, heading the same direction. One travels at 60 miles per hour, and the other travels at 45 miles per hour. In how long will the fast car be 90 miles ahead of the slower car.


2) Find two consecutive even integers so that the sum of the first, and 4 times the second number is 158.

My friends told me they were easy but I can't figure them out .

Answer 1

let t be the time it takes both car to be 90 miles a part.
So after t hours, the distance the car that goes at 60 mi/hr will 90 miles more than the distance the car goes at 45 miles

fast car = slow car + 90

distance = speed * time

fast car:
d = 60t

slow car
d = 45t

60t = 45t + 90
15t = 90
t = 6hrs


2)
let x be the first integer
x + 2 is the next even integer

4 times the second even integer:
4(x + 2)

sum means addition

x + 4(x + 2) = 158
x + 4x + 8 = 158
5x = 150
x = 30

30 and 32

hope this helps

Answer 2

1) if x = the time we are looking for:

60x = 45x + 90
15x = 90
x = 6 hours

Check: after 6 hours, car 1 would have travelled 60*6 = 360 miles, car 2 would have travelled 45*6 = 270 miles

2) the two integers would be x and x+2, such that:

x + 4(x+2) = 158
x + 4x + 8 = 158
5x + 8 = 158
5x = 150
x = 30

so the two numbers are 30 and 32

Check: 30 + 4(32) = 30 + 128 = 158

Hope this helps! :)

Answer 3

1.)
60x = 45x + 90
15x = 90
x = 6 hours

2.)
x=first integer
x+2=second integer

x+4(x+2)=158
x+4x+8=158
5x=158-8
5x=150
divide both sides by 5
x=30

first integer=30
second integer=32

Answer 4

The first one is 60a -45a = 90
15a = 90
a = 90/15
a = 6 hours

Don't know the second one, sorry