SOLUTION: Can you please help me write out and solve the equation for this word problem? A car leaves a town traveling at 60 miles per hour. How long will it take a second car traveling a

Question 203094: Can you please help me write out and solve the equation for this word problem?
A car leaves a town traveling at 60 miles per hour. How long will it take a second car traveling at 75 miles per hour to catch up to the first car if it leaves 2 hours later?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's make t = time (in hours) that the first car travels.

First, let's set up the equation for the first car to leave. Recall that the distance "d" equals the speed "r" multiplied by the time "t". So this means that

Plug in (the speed of the first car)

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Now let's set up the second equation (for the second car). Since the first car travels "t" hours, and it has a 2 hour head start, this means that the second car is going to travel "t-2" hours (eg, the first car travels t=6 hours and the second travels t-2=6-2=4 hours).

So this means that we start with and plug in and replace "t" with "t-2" to get

Note: the "d"s of both equations are the same "d" since the cars will have gone the distance when they meet.

So we have the two equations and

Start with the first equation.

Plug in

Distribute.

Add to both sides.

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

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Answer:

So the solution is which means that the first car traveled for 10 hours

Subtract 2 from this answer to get . So this tells us that the second car traveled 8 hours.

So it takes 8 hours for the second car to catch up and meet the first car.
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