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

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 [tex]Distance=Rate* Time[/tex] formula to solve this problem.

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

Train B: [tex]D_b=R*4[/tex]

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

[tex]D_a+D_b=585[/tex]

[tex]2.5R+4R=585[/tex]

[tex]6.5 R=585[/tex]

[tex]R=\frac{585}{6.5}[/tex]

[tex]R=90[/tex]

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

kudzordzifrancis kudzordzifrancis · Answer 2 · 2018-10-25T09:55:39+02:00

The total distance between the two stations is

[tex]585 miles[/tex]

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

[tex](585 - x) \: miles[/tex]

[tex]speed=\frac{distance}{time}[/tex]

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

For train a,

[tex]speed=\frac{585 - x}{4 } ....eqn \: 1[/tex]

For train b,

[tex]speed=\frac{x}{2 \frac{1}{2} } .....eqn \: 2[/tex]

We were told that both trains traveled with the same speed

This means that eqn 1 = eqn 2

[tex]\frac{585 - x}{4 }=\frac{x}{2.5} [/tex]

Cross multiplying

[tex]2.5(585 - x)=4(x) [/tex]

Expanding the brackets

[tex]1462.5 - 2.5x =4x[/tex]

Grouping like terms

[tex]1462.5= 4x + 2.5x[/tex]

[tex]6.5x = 1462.5 \\ x = \frac{1462.5}{6.5 } =225 \: miles[/tex]

The speed at which the trains were travelling is

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

Hence the rate of the trains is

[tex]=90\: miles /hour[/tex]