Math - Rates word problem

[ZenoVT]

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How long will two trains 520 m and 280 m long and traveling 38 and 30 km/hr, respectively, take to pass one another completely when they are traveling in the same direction?



Can anybody help me visualize this question and how to solve it? Thanks!
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[jjw822]

i think we need to know the position of both trains respect to each other..

But anyways, I would change km/h to m/h or m/min then go from there

 

[klutzy1987]

based on the way this question is worded i would say it is 38x=30x+(280/1000). That is assuming that both trains start from the same spot.

 

[Streetwolf]

How long will two trains 520 m and 280 m long and traveling 38 and 30 km/hr, respectively, take to pass one another completely when they are traveling in the same direction?



Can anybody help me visualize this question and how to solve it? Thanks!
​

The only way you get an answer is if the slower train is initially in front. The slower train is traveling 30 km/hr and is 280 m long (0.28 km). The faster train is traveling 38 km/hr and is 520 m long (0.52 km). The faster train is essentially traveling at 8 km/hr compared to the slower train not moving (why?).

When the faster train's front end is at the same spot as the slower train's back end, the timer begins. The faster train's front end needs to travel 520 meters before its back end is where its front end was. After it travels 520 meters then its back end will be even with the back end of the slower train. Now the back end of the faster train needs to travel the length of the slower train (280 meters) in order to fully pass it. So it needs to travel a total of 800 meters = 0.8 km. If it is traveling 8 km/hr faster than the slower train is, and it needs to travel 0.8 km, then it will take 0.8 km / 8 km/hr = 1/10 hr to pass it fully. That's 6 minutes.

 

[ZenoVT]

Thanks a bundle guys. I understand now. The time starts when the longer train is at the same point as the rear end of the shorter train.

 

[ZenoVT]

I'm having trouble understanding this problem as well:
If Sarah can do a work in 8 days and Julie can do the same work in 12 days, which of the combinations given below can complete the work in the least amount of time?

CDM says -C.40% work done by Sarah and the rest by Julie- is the correct answer

Since they are doing the work at the same time which will give the least amount of time, wouldn't Sarah who could do the work faster do more work than Julie?

 

[PooyaH]

I'm having trouble understanding this problem as well:
If Sarah can do a work in 8 days and Julie can do the same work in 12 days, which of the combinations given below can complete the work in the least amount of time?

CDM says -C.40% work done by Sarah and the rest by Julie- is the correct answer

Since they are doing the work at the same time which will give the least amount of time, wouldn't Sarah who could do the work faster do more work than Julie?

Let the whole work be 20 (12 + 8)

Sarah = 8/20 or 2/5 or 40%

 

[ZenoVT]

Where did you 8/20?

 

[ZenoVT]

If I let the total amount of work = 20 then wouldn't the equation be:
20 = 1/8 t + 1/12 t
20 = t (1/8 + 1/12)
20 = t (5/24)
t = 24(4) = 96
Amount of work Sarah does = 1/8 t = 96/8 = 12
Amount of work Julie does = 1/12 t = 96/12 = 8
12:8 => 6:4 so would Sarah be 60% and Julie be 40%

 

[PooyaH]

Where did you 8/20?

Sarah completes a work in 8 days and Julie does the same amount of work in 12 days, so you can assume the whole work is 12 + 8 = 20 or (20/20)

Since Sarah does the work in 8 days, then she would do 8/20 of the work! which is the same thing as 40%
Julie does 12/20 of the work, which is the same thing as 60%

For these type of problems use this:
(AB)/(A+B) so, (12x8)/(12+8) = 4.8 hrs

 

[ZenoVT]

Oh so basically Sarah is only working for 8 days while Julie is working for 12 days. I see, I thought they would be working the same amount of times. I'm terrible with math.

 

[PooyaH]

Oh so basically Sarah is only working for 8 days while Julie is working for 12 days. I see, I thought they would be working the same amount of times. I'm terrible with math.

It's ok just keep practicing!

 

[ZenoVT]

Thanks PooyaH