Question

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 heading 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

Answer 1

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.

Answer 2

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  

$=90\: miles /hour$