Question

Two cars leave towns 340 kilometers apart at the same time and travel toward each other. One car's rate is 18 kilometers per hour more than the other's. If they meet in 2 hours, what is the rate of the faster car?

Two cars leave towns
340
kilometers apart at the same time and travel toward each other. One car's rate is
18
kilometers per hour more than the other's. If they meet in
2
hours, what is the rate of the faster car?

Answer 1

94 km/hr

Explanation:

We have two cars heading towards each other. They start 340 km apart and meet up 2 hours later. This means that they are traveling:

`340/2=170` km/hr towards each other.

If the two cars were traveling the same speed, they'd both be going:

`170/2=85` km/hr

We know that one car is traveling 18 km/hr faster than the other car. One way we can account for this is to `pm9` km/hr to the average speed:

`85 pm 9 = 94, 76` km/hr

And so the faster car travels `94xx2=188` km while the slower car travels `76xx2=152` km, for a total of `188+152=340` km.

Answer 2

The rate of the faster car is `94` kilometers per hour

Explanation:

Let `x` represent the rate of speed of the slower car.

Slower car . . . . . . . `x` `larr` speed of slower car
`18` kph faster . . . . ..`x + 18` `larr` speed of faster car

In two hours, they travel `340` km
Therefore, in one hour they travel `170` km

[speed of slower car] + [speed of faster] = [ 170 ]
[ . . . . . . . . `x` . . . . . . . .] + [ . . . `x + 18` . . . ] = [ 170 ]

`( x ) + ( x + 18) = 170`

1) Combine like terms
`2x + 18 = 170`

2) Subtract `18` from both sides to isolate the `2x` term
`2x = 152`

3) Divide both sides by `2` to isolate `x`, already defined as "the speed of the slower car"
`x = 76`, already defined as "the speed of the slower car"

Therefore the faster car was going at the speed of
`76 + 18`
`color(white)(....)` `94` kilometers per hour `larr` answer for "speed of faster car"

Answer:
The rate of the faster car is `94` kilometers per hour

`color(white)(-----)` . . . . . . . . . . . . .

Check

`2` hours @ `76` kilometers per hour . . . . `152` kph
`2` hours @ `94` kilometers per hour . . . . `188` kph
.................... `color(white)(mmmmmmmmmmm.)...............`
Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . `340` kph

`Check`