# distance=rate*t

#### needhelpmom

##### New member
At a NASCAR race track, the distance per lap is 2 miles. Lou drives his car at a constant rate of 160 miles per hour.

Ralph drives his car at a constant rate of 170 miles per hour. How long will it take before Ralph gains 2 laps in relation to Lou?

do not know how to figure these word problems out and write an equation can you help me

#### ting

##### Junior Member
See if you can make sense of this.

No of laps = distance/2

Distance = rate * time

No. of laps = rate/2 *time

Equate the number of laps done by Ralph in t hours with the number of laps done by Lou in t hours plus 2.

170/2*t = 160/2*t + 2

Solve for t

85t = 80t + 2

5t = 2

t = 2/5

So it takes 2/5 of an hour.

2/5 *60 = 24 minutes.

Check!

Calculate the number of laps each does in 24minutes.

(170 * 24/60)/ 2 = 34

(160 * 24/60)/2 = 32

Edit: Galactus' approach is better! I'll leave this up as an example of how you can over complicate these thing

#### galactus

##### Super Moderator
Staff member
Since distance equals rate*time, we must find out how long it takes until Ralph has 4 miles (2 laps) on Lou.

We could write this as:

160t+4=170t, solve for t.

Once you find t, check your answer. Multiply it by 160 and 170, respectively, and see if there is a difference of 4 miles.

#### needhelpmom

##### New member
Thanks/ yes it makes since to me now.