trains' speeds / driving speed / plane's speed / interest

[dkarolasz]

1.Science and medicine. A passenger train can travel 325 mi in the same time a freight train takes to travel 200mi. If the speed of the passenger train is 25 mi/h faster the the speed of the freight train, find the speed of each.

2. Ariana took 2 h longer to drive 360 mi on the first day of a trip that she took to drive 270 mi on the second day. If her speed was the same on both days, what was the driving time each day?

3. A plane flies 720mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air?

4. Kevin earned $165 interest for 1 year on an investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?

 

[jonboy]

Hello, dkarolasz!

1.Science and medicine. A passenger train can travel 325 mi in the same time a freight train takes to travel 200mi. If the speed of the passenger train is 25 mi/h faster the the speed of the freight train, find the speed of each.

So the times are equal, let them be \(\displaystyle t\). Let the speed be \(\displaystyle s\).

Also this formula is true: \(\displaystyle \L \;d\,=\,s\,\cdot\,t\)

.....\(\displaystyle d\,=\,distance\)

So you can create these formulas.

....Passenger train: \(\displaystyle \L \;325\,=\,(s\,+\,25)(t)\)

....Freight train: \(\displaystyle \L \;200\,=\,(s)(t)\)

Solve the system for \(\displaystyle \,s\,\), which is speed.

2. Ariana took 2 h longer to drive 360 mi on the first day of a trip that she took to drive 270 mi on the second day. If her speed was the same on both days, what was the driving time each day?

We'll use the same formula.

....First day: \(\displaystyle \L \;360\,=\,(s)(t\,+\,2)\)

....Second day: \(\displaystyle \L \;270\,=\,(s)(t)\)

Solve for \(\displaystyle \,t\,\), which is time.

4. Kevin earned $165 interest for 1 year on an investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?

Use the famous interest formula:\(\displaystyle \L \;i\,=\,prt\)

....\(\displaystyle i\,=\,interest\,,\,p\,=\,price\,,\,r\,=\,rate\,,\,t\,=\,time\)

So we have for the first part:\(\displaystyle \L \;165\,=\,(1500)(r)(1)\,\Rightarrow\,r\,=\,.11\,=\,11%\)

Then the second part:\(\displaystyle \L \;i\,=\,(2500)(.11)(t)\)

I don't see how you can simplify this more since you aren't given a time. This is all I can help you on.

 

[dkarolasz]

ok

1. 40 for the speed of the train
2. 45 mph Ariana drove
4. $275 on interest kevin earned

 

[tkhunny]

I am not encouraged. You show now work. You show signs of just guessing. I have no confidence that you are learning anything.

 

[Mrspi]

Re: a couple of more word problems...

1.Science and medicine. A passenger train can travel 325 mi in the same time a freight train takes to travel 200mi. If the speed of the passenger train is 25 mi/h faster the the speed of the freight train, find the speed of each.

time = distance / rate

Let r = rate of the freight train. The time for the freight to travel 200 miles is 200/r.

Then r + 25 is the rate of the passenger train. The time it takes this train to travel [325 miles is 325/(r + 25).

You're told the two times are the same, so
200/r = 325/(r + 25)

Solve for r.....

2. Ariana took 2 h longer to drive 360 mi on the first day of a trip that she took to drive 270 mi on the second day. If her speed was the same on both days, what was the driving time each day?

Let r = rate

360/r is the time it took to drive 360 miles the first day.
270/r is the time it took to drive 270 miles the second day.

time on first day = time on second day, + two hours
360/r = (270/r) + 2

Solve for r.....

3. A plane flies 720mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air?

Let r = rate of plane in still air.

Flying AGAINST the wind, the rate is r - 30 (because the headwind decreases the plane's speed). It will take 720 / (r - 30) hours to fly 720 miles.

Flying WITH the wind, the rate is r + 30 (because the tailwind increases the plane's speed). It will take 720 / (r + 30) hours to fly 720 miles.

The total time for the round trip is 10 hours. So,

[720 / (r - 30)] + [720 / (r + 30)] = 10

Solve for r.

4. Kevin earned $165 interest for 1 year on an investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?
[/b]

Since the rate and time are the same, you can write a proportion:

interest / investment = interest / investment

$165 is earned on $1500. Let x = amount earned on $2500:

165 / 1500 = x / 2500

Solve for x.....

 

[dkarolasz]

tk hunny,

I'm sorry I'll show you the work,

1.pass train 325=(s+25)(t) 325=(40+25)(5)
freight train 200= (s)(t) 200=(40)(5)


2. 360= (s)(t+2) (45)(6+2)
270=(s)(t) (45)(6)

4. 165=(1500)(r)(1) > .11= 11%
(2500)(.11) = $275 in interest

 

[dkarolasz]

I'm having a hard time with number 3.


[720 / (r - 30)] + [720 / (r + 30)] = 10

Solve for r.

I did 720 = r-30
+30 +30
_______________
750 = r


720 = r+30
-30 -30
___________

690 = r


I'm not getting it...