Distance Rate Time: how long for faster car to catch up?

[rytesideup]

Please help.

Suppose you are driving 50 mph and you are 9 miles ahead of a car pursuing you at 70 mph. How many minutes will it take for the pursuit car to catch up to you?

I know rate is 50 & 70
I think time is t
I think distance 50t & 70t

Please help.

 

[Loren]

Re: Distance Rate Time

You're good so far. Keep going.

Draw a sketch.

......9 mi.............................50t
.................|-------------------------------------------------->

|---------------------------------------------------------------->
...............................70t

Build your equation on basis that the two distances pictured are equal.

Just remember that the distance is in miles per HOUR and the time wanted is in MINUTES.

 

[rytesideup]

Re: Distance Rate Time

O.k. I have set the 2 equations equal and after reducing it to minutes I have come up with 27 mins. I am the mom many years removed from algebra. Please advise.

thanks

 

[kasie-tutor]

Re: Distance Rate Time

Dear rytesideup,

This is what I'd be asking myself after getting an answer:

Is the answer reasonable (not too far from what I would have guessed)? Does it make the equation true (does it check)?

Plug your answer into both sides of your equation and solve both sides. If they come out to the same answer, then your answer checks.

[The answer I got is a 2-digit multiple of three].

 

[nycfunction]

Please help.

Suppose you are driving 50 mph and you are 9 miles ahead of a car pursuing you at 70 mph. How many minutes will it take for the pursuit car to catch up to you?

I know rate is 50 & 70
I think time is t
I think distance 50t & 70t

Please help.

Both cars are going in the same direction. This indicates that distances are equal.

Let t = time (in hours) for the pursuit car to catch up with you.

Use distance = rate (time).

Minutes cannot be used in D = rt problems because rate is in miles per hour.

Can you finish now?

 

[Denis]

Re: Distance Rate Time

O.k. I have set the 2 equations equal and after reducing it to minutes I have come up with 27 mins. I am the mom many years removed from algebra. Please advise.

CORRECT mom; good job.

You can also take this short-cut:
9 miles to be made up, at net speed of 20 mph (70 - 50):
9 / 20 = .45 hour : .45 * 60 = 27 minutes

 

[rytesideup]

Thank you everyone for all of your help. I wish I had this much fun when I was actually a student. Again, thanks!!!! :lol: