Word problem

[shenikathomas]

Two cars start at an interstate interchange and travel in the same direction at average speeds of 40 miles per hour and 55 miles per hour. How much time must elapse before the two cars are 5 miles apart?

 

[soroban]

Hello, shenikathomas!

Two cars start at an interchange and travel in the same direction at average speeds of 40 mph and 55 mph.
How much time must elapse before the two cars are 5 miles apart?

Here's a back-door approach . . .

The cars are separating at the rate of: 55 - 40 = 15 mph.

To be 5 miles apart, it will take 1/3 of an hour = 20 minutes.

 

[Gene]

You may have heard a rumor that distance = velocity times time. The relative velocity between the two cars is 15 MPH.
D=VT
5=15T
Solve for T

Or
D₁ = 40T
D₂ = 55T
D=D₂-D₁
5 = 15T

 

[Corsair_cavalier]

.

How much time must elapse before the two cars are 5 miles apart?

To be completely technical... any amount of time less than when they are actually 5 miles apart could be your answer. Therefore,
T<D/V
T<5/15
T<1/3
and since we know they aren't travelling through any black holes or anything, we know that T must be positive.