Jaden and Dani are both travelling by train. Jaden's train travels 130 km in 75 minutes.
Dani's train travels 312 km.
It leaves at 15:15 and arrives at 18:30.
Work out the difference, in km/h, between the average speed of their trains.

 28.765957 km/hour

This value is approximate. Round it however you need to.

Explanation:

Let's convert 75 minutes to hours.

75 min = (75 min)*(1 hr/60 min) = (75/60) hr = 1.25 hr

So Jaden's train takes 1.25 hours to travel 130 km. Her train's speed is

speed = distance/time

speed = (130 km)/(1.25 hrs)

speed = (130/1.25) km per hour

speed = 104 km per hour

Let A = 104, so we can use it later.

Dani's train leaves at 15:15 and arrives at 18:30. We need to calculate the duration of elapsed time here.

Overall, the length of time from 15:15 to 18:30 is 0.75+2+0.5 = 3.25 hours.

Dani's train travels 312 km in 3.25 hours.

That train's speed is...

speed = distance/time

speed = (312 km)/(3.25 hours)

speed = (312/2.35) km per hour

speed = 132.765957 km per hour, approximately

Let B = 132.765957 so we can use it later.

Lastly, we subtract the values of A and B to get the final answer

C = difference in train speeds.

C = B - A

C = 132.765957 - 104

C = 28.765957 km/hour

This value is approximate. This says that Dani's train is approximately 28.765957 km/hour faster compared to Jaden's train.

The value of sin Θ is:

                   12/13

We know that the sine trignometric ratio corresponding to a given angle Θ is defined as the ratio of the side opposite to the given angle to the hypotenuse of the triangle.

i.e. sin Θ=AB/BC

Since AB is the side opposite to Θ

and the hypotenuse of the right triangle is: BC

                        Hence, we have:

                           sin Θ=12/13