Math Help !!

[swanmom]

Ok, all you math wizards out there. This is part of DD's homework and, if someone could explain it to me, then I can try to help her.
Here's the problem:

Don, Ed and Frank are in a race. At one point, Don is 50 yards behind Ed, and Ed is 150 yards behind Frank. They are all going at a constant speed.

It takes 8 minutes for Don to overtake Ed, and another 8 minutes for Don to overtake Frank. From this starting position, in how many minutes will Ed overtake Frank.

Don..............Ed................................................Frank



I'd be so appreciative if someone could take the time to help with this.

 

[disney funseeker]

well, I don't know the answer but just wanted to know what grade math I can't do.

 

[Kimberly]

Ah high school physics. Wait until she takes the AP test and finds out that most colleges will want her to take their version of physics, so it feels like a complete waste of time.

Anyways, back to the problem. Relative to Ed, Don takes 8 minutes to cover a 50 yard difference, assuming that Ed runs at a constant velocity. With respect to Frank, Ed covers 100 yards in 8 minutes.

Does that mean that Don was accelerating? Did Don speed up instantaneously when he got past Ed? I think I'm looking too much in a simple problem, but I need more information. It's been 4 years since I last took
physics...

 

[ElizaB39]

Ok, all you math wizards out there. This is part of DD's homework and, if someone could explain it to me, then I can try to help her.
Here's the problem:

Don, Ed and Frank are in a race. At one point, Don is 50 years behind Ed, and Ed is 150 yards behind Frank. They are all going at a constant speed.

It takes 8 minutes for Don to overtake Ed, and another 8 minutes for Don to overtake Frank. From this starting position, in how many minutes will Ed overtake Frank.

Don..............Ed................................................Frank



I'd be so appreciative if someone could take the time to help with this.

Hmmm, he won't because Don is moving in "years" and Ed is moving in "yards"? Hmm he won't because Ed and Frank are moving at the same speed? Don is moving at a speed of 100 yards per 8 minutes; it takes him 16 minutes to go 200 yards, right? That is all I can figure out. Ed is also moving as Don is overtaking him, but I DON"T KNOW! Help me and save me from story problems. Wait I'll ask my daughter to help me. Oops she is in bed already. No go.

 

[ElizaB39]

Ah high school physics. Wait until she takes the AP test and finds out that most colleges will want her to take their version of physics, so it feels like a complete waste of time.

Anyways, back to the problem. Relative to Ed, Don takes 8 minutes to cover a 50 yard difference, assuming that Ed runs at a constant velocity. With respect to Frank, Ed covers 100 yards in 8 minutes.

Does that mean that Don was accelerating? Did Don speed up instantaneously when he got past Ed? I think I'm looking too much in a simple problem, but I need more information. It's been 4 years since I last took
physics...

All moving at constant speed. I figured that they were all moving so the one guy who overtook everyone moved at a speed of 200 yards per 16 minutes, or 100 yards per 8 minutes. I THINK that is right, right?

 

[Kimberly]

My guess would be 16 minutes, assuming that Frank is running at half the speed Ed is, and Don is running at twice the speed Ed is.

So it will take 2 times the amount of time for Ed to pass Frank than it did Don to go from Ed to Frank.

 

[ElizaB39]

The middle guy is moving at 50 yards per 4 minutes, no that is the same as 100 yards per 8 minutes the same as the overtaker, it doesn't make sense to me, why why why?

 

[Kimberly]

Jeez... Physical Chemistry was less of a pain than this question... grrr...

 

[melanie18]

i'm so old...

 

[ElizaB39]

It takes Ed 8 minutes to go 50 yards, he gets overtaken at yard 100 by Don who is movingg at 100 yards per 8 minutes. it will take him 24 minutes to go 150 yards and overtake the guy in the front.

Let me know if this is right.

 

[golfgal]

I have know idea what the answer is but BOY ARE THEY SLOW!!! 24 minutes to go 150 yards, that is like walking a block in 24 minutes. Maybe the answer is that they are turtles????

 

[damo]

Here is a full solution:

Let D represent Don's speed. Let E represent Ed's speed. Let F represent Frank's speed.

After 8 seconds, Don and Ed have travelled the same distance. Using the fact that distance = time x speed: 8D = 8E +50 so E = (8d-50)/8

After 16 seconds, Don and Frank have travelled the same distance. 16D= 16F + 200 or F = (16D-200)/16 or F = (8D - 100)/8

We want to know when Ed and Frank will have travelled the same distance. Let that time be t. Then (t)(E) +50 + t(F) +200

Substitute from above to get: [(t)(8d-50)/8] +50 = [(t)(8D-100)/8] +200

Solving this yields that t=24.

 

[ErikdaRed]

8d = 8e+ 50 ==> e = (8d - 50)/8
16d = 16f + 200 ==> f = (16d - 200)/16


ne = nf + 150
n(e-f) = 150
n[(8d-50)/8 - (16d - 200)/16] = 150
n[(8d - 50 -8d + 100)/8] = 150
n[50/8] = 150
n = 24 minutes

 

[paigevz]

Ummm..........24?

I am just thinking that Frank is going three times faster than Ed, since it took Don the same speed in three times farther. So, it should take Ed three times longer to overtake Frank than it took Don?

Oh, and ElizaB39 thinks so too!

 

[damo]

oopsie

 

[paigevz]

No, I'm answering Ed, the guy 150 yards behind Frank. Don passed Frank in 8 minutes from 150 yards back.

 

[ElizaB39]

We know it takes 16 minutes for the last guy to overtake the first guy, and the last guy is 200 yards behind the first guy so it takes him 16 minutes to go 200 yards, right?

Okay, then the last guy overtakes the middle guy at 8 minutes, so the last guy has moved 100 yards, then the middle guy has moved 50 (he was already 50 ahead of the last guy at the start of the problem). Thus the middle guy is moving at 50 yars per 8 minutes. he has 150 yards to voer before he overatkes the guy in front, 8 minutes x 3 (150/50) = 24 minutes.

I THINK!

 

[ElizaB39]

Ummm..........24?

I am just thinking that Frank is going three times faster than Ed, since it took Don the same speed in three times farther. So, it should take Ed three times longer to overtake Frank than it took Don?

Oh, and ElizaB39 thinks so too!

Well, we must be right then, right?

 

[paigevz]

Yes, unless we're both just using the same fallacy of logic in working this out!