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Grace [21]
3 years ago
5

Train a And train b leave Central Station at the same time they travel the same speed but in opposite direction with a train a h

eading towards Station a and train b heading towards station b train a Reaches station after 2 1/2 hours train b reaching station be after four hours you station A and b Station are 585 miles apart what is the rate of the trains

Mathematics
2 answers:
kramer3 years ago
6 0

Answer:

Both trains are traveling at 90 miles per hour.

Step-by-step explanation:

We are told that the rate is the same for both trains, and we know that the distance traveled by train a plus the distance traveled by train b equals 585 miles.

We will use Distance=Rate* Time formula to solve this problem.

Train A: D_a=R*2.5 (Using 2.5 instead of 2 and 1/2)

Train B: D_b=R*4

We can set an equation to solve for rate R of trains as:

D_a+D_b=585

2.5R+4R=585

6.5 R=585

R=\frac{585}{6.5}

R=90

Therefore, rate of both train a and train b is 90 miles per hour.



natali 33 [55]3 years ago
5 0

The total distance between the two stations is


585 miles


Let the distance between the Central Station and station b be x



This implies that the distance between the Central Station and station a is


(585 - x) \: miles


speed=\frac{distance}{time}


so, let us write equations in terms of speed for the two trains and solve


 For train a,


speed=\frac{585 - x}{4 } ....eqn \: 1


For train b,


speed=\frac{x}{2  \frac{1}{2} } .....eqn \: 2


We were told that both trains traveled with the same speed



This means that eqn 1 = eqn 2


\frac{585 - x}{4 }=\frac{x}{2.5}


Cross multiplying


2.5(585 - x)=4(x)


Expanding the brackets


1462.5  - 2.5x =4x


Grouping like terms


1462.5= 4x + 2.5x


6.5x = 1462.5 \\ x = \frac{1462.5}{6.5 } =225 \: miles


The speed at which the trains were travelling is



\frac{225}{2.5}= 90 \: miles /hour


Hence the rate of the trains is  


=90\: miles /hour



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