Question

Two cars leave towns
540
kilometers apart at the same time and travel toward each other. One car's rate is
20
kilometers per hour less than the other's. If they meet in
3
hours, what is the rate of the slower car?
Do not do any rounding.

Answer 1

we need equations
they ask for
what is the rate of the slower car?

the first thing is to give this unknown a name. for example x

so let the speed of the slower car be x

One car's rate is 20 kilometers per hour less than the other's.

any idea what the speed of the fast car is ? (using x as part of the answer)

Answer 2

20 - x

Answer 3

to think about it (more clearly)
say (for example), the fast car goes 50 kph. how fast will the slow car go
if One car's rate is 20 kilometers per hour less than the other's.

Answer 4

20 less than 50?

Answer 5

yes. and do understand that, think about this:
1 less than 2. what is that ?

Answer 6

1

Answer 7

minus

Answer 8

yes. 1 less than 2 means the same as 2-1
so 50-20 is what 20 less than 50 means

Answer 9

oh ok

Answer 10

so what would be the equation for this problem?

Answer 11

if we use words:
slow car is 20 kph less than fast car

if we make that look more like math
slow car = fast car - 20 kph

if we use x for the speed of the slow car:

x = fast car - 20 kph

if we add 20 to both sides we get
x+20 = fast car

which means the speed of the fast car is x+20 i..e 20 kph faster than the slow car.

Answer 12

next, we use

rate * time = distance

if the rate (speed) of the slow car is x
and it drives for 3 hours
(I used If they meet in 3 hours, which tells us how long it drove)
how far did it go ? can you write the "math expression" ?

Answer 13

x times 3

Answer 14

yes, or 3x (in algebra we usually put the number first, and leave out the multiply sign)

Answer 15

meanwhile how far did the fast car go ?
remember, its speed is (x+20)

Answer 16

stuck ?

Answer 17

the fast car goes for 3 hours, at a rate of (x+20)
show those being multiplied to get the "distance"

Answer 18

so its 3x + (x+20

Answer 19

3*(x+20) is the distance of the fast car
or (leaving out the multiply sign *)

3(x+20)

Answer 20

Two cars leave towns 540 kilometers apart at the same time and travel toward each other.

that means when they meet, they together traveled 540