The distance between New York City, NY, and Louisville, KY is 720 miles. One morning a train traveling 80 mph left from New York. Two hours later a slower train, traveling at 60 mph, left Louisville. How many hours will the slower train travel for before both trains will arrive at the same point?

Respuesta :

Answer:

2 hours

Step-by-step explanation:

Given : The distance between New York City, NY, and Louisville, KY is 720 miles. One morning a train traveling 80 mph left from New York. Two hours later a slower train, traveling at 60 mph, left Louisville.

To find : How many hours will the slower train travel for before both trains will arrive at the same point?

Solution : Let the distance covered by NY is x

and  let the distance covered by KY is y

Total distance covered is  [tex]x+y=720[/tex]   ........[1]

→ New York city,

Distance traveled = x

Speed of the train = 80 mph

Time taken = t+2

Formula is [tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]

[tex]t+2=\frac{x}{80}[/tex] .......[2]

→ Louisville,

Distance traveled = y

Speed of the train = 60 mph

Time taken = t

Formula is [tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]

[tex]t=\frac{y}{60}[/tex] .......[3]

Put the value of t from [3] into [2]

[tex]\frac{x}{80}- \frac{y}{60}=2[/tex]  ......[4]

Now, we solve equation [1] and [4],

Put the value of y from [1] and put back in [4], [tex]y=720-x[/tex]

[tex]\frac{x}{80}- \frac{y}{60}=2[/tex]

[tex]\frac{x}{80}- \frac{720-x}{60}=2[/tex]

[tex]\frac{60x-80(720-x)}{80\times60}=2[/tex]

[tex]60x-57600+80x=9600[/tex]

[tex]140x-57600=9600[/tex]

[tex]140x=57600+9600=67200[/tex]

[tex]x=\frac{67200}{140}=480[/tex]

Put x=480 in [1]

[tex]x+y=720[/tex]  

[tex]480+y=720[/tex]  

[tex]y=240[/tex]  

So, The distance covered by train from New York city is x=480 miles

The distance covered by train from Louisville is y=240 miles.

Now put value of y in [3] to get time,

[tex]t=\frac{y}{60}[/tex]

[tex]t=\frac{240}{60}[/tex]

[tex]t=4[/tex]

So, The time taken by train from Louisville is 4 hr.

The time taken by train from New York city is t+2=4+2=6 hr.

6-4=2 hours will the slower train travel for before both trains will arrive at the same point.




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