Question

A car passes a landmark on a highway traveling at a constant rate of 45 kilometers per hour. One hour later, a second car passes the same landmark traveling in the same direction at 65 kilometers per hour. How much time after the second car passes the landmark will it overtake the first car?

Do not do any rounding.

Answer 1

@iGreen

Answer 2

Let them meet at distance x
Car 1 speed= 45 mph
Car 2 speed = 65 mph

Time when they cross = 1.00 hour

Time taken by Car 1 = \(\dfrac{x}{45}\)

Time taken by Car 2 = \(\dfrac{x}{65}\)

That means the difference between Car 1 and Car 2 is 1:

\(\dfrac{x}{45} - \dfrac{x}{65} = 1\)

Now let's convert the fractions.

The LCD between these two fractions is 585.

Now let's multiply the equation by 585:

\(\dfrac{585}{45x} - \dfrac{585}{60x} = 1 \cdot 585\)

Simplify:

\(13x - 9x = 585\)

Subtract:

\(4x = 585\)

Divide:

\(x = 146.25mi\)

Car 2 Speed = 65 mph
Distance = 146.25
Time taken = \(146.25 \div 65\)

So what's 146.25 / 65? @dontsmileurugly

Answer 3

2.25

Answer 4

Yep, so that's your answer.