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sergiy2304 [10]
3 years ago
14

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?
Mathematics
1 answer:
beks73 [17]3 years ago
7 0

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  x+y=720   ........[1]

→ New York city,

Distance traveled = x

Speed of the train = 80 mph

Time taken = t+2

Formula is \text{Time}=\frac{\text{Distance}}{\text{Speed}}

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

→ Louisville,

Distance traveled = y

Speed of the train = 60 mph

Time taken = t

Formula is \text{Time}=\frac{\text{Distance}}{\text{Speed}}

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

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

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

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

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

\frac{x}{80}- \frac{y}{60}=2

\frac{x}{80}- \frac{720-x}{60}=2

\frac{60x-80(720-x)}{80\times60}=2

60x-57600+80x=9600

140x-57600=9600

140x=57600+9600=67200

x=\frac{67200}{140}=480

Put x=480 in [1]

x+y=720  

480+y=720  

y=240  

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,

t=\frac{y}{60}

t=\frac{240}{60}

t=4

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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