-Tom and Jerry, who are 568 miles apart,

Question

Here is one---Tom and Jerry, who are 568 miles apart, start driving toward each other in their cars. Tom drives 40 mph and Jerry drives 36 mph, How soon will they meet if Tom has an accident and is delayed one hour before continuing his trip?

Answer 1

Remember that distance = (rate)(time). We can write one equation for Tom's drive and another for Jerry's. Tom's is a bit more complicated, since he had an accident, so let's start with Jerry.

 

 

 

JERRY'S DRIVE:

We don't know how far Jerry drives before he meets Tom, so call the distance d. He drives at a rate of 36 mph. We don't know how long he drives before he meets Tom, so call the time t.

 

d = 36t

 

 

 

TOM'S DRIVE:

 

We don't know how far Tom drives before he meets Jerry, but their combined distances need to equal 568 miles. So, he drives 568 - d miles. He drives at a rate of 40 mph. We don't know how long Tom drives before he meets Jerry, but we do know that, since he's delayed for an hour, his actual driving time is one hour less than Jerry's. So, call his time t - 1.

 

568 - d = 40(t - 1)

 

 

 

Now you have a system of two equations:

 

d = 36t

568 - d = 40(t - 1)

 

Plug the first equation into the second equation and solve for t:

 

568 - d = 40(t - 1)

568 - 36t = 40(t - 1)

568 - 36t = 40t - 40

608 - 36t = 40t

608 = 76t

8 = t

 

Tom and Jerry will meet in t = 8 hours.

 

 

 

Let's check our work. In 8 hours, Jerry drives 36(8) = 288 miles. In 8 hours, with a 1-hour accident, Tom drives 40(7) = 280 miles. Together, that's 288 + 280 = 568 miles.

 

That checks out!