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.