Can you explain this, how will I be able to find it?

Question

Towns A & B are 80 KM apart. A couple arranges to drive from town A & meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for 2.50 hrs. in the directions show (the gave me a pic- looks like a triangle). Car 1 has a speed of 90 km/h. If the cars drive simultaneously at the lake, what is the speed of car 2?

how would I find the speed of car 2 if car 1 is 90 km/h.... would I do Vy=gt... but it doesn't make sense...?

Answer 1

Since car 1 drove for 2.5 hours at 90 km/h, car 1 went 225 km. So it's clear that L is not on the line between A and B, and that the distance from A to L is 225 km. The distance from A to B is 80 km. There must be something in the picture that tells you one additional piece of information about the triangle ALB, that will allow you to calculate the distance from B to L. That distance, divided by 2.5 hours, is the speed of car 2.

Answer 2

As you have been given a picture containing a triangle. You know which side of the triangle is 80km, another you can calculate as 90x2.5 = 225 km as the last answerer has done. Measure the angle between these sides call it y. Then the third side, T would be given by Cosine formula as

T = Sqrt[80x80+225x225-2x80x225xCos y]

Divide this T by 2.5 hrs and you would get the speed of the car 2

Alternatively you can use the similarity property of triangles to get the result. Let distance between towns be D = 80 km, The distance between town A and Lake be L= 225, And the unknown distance between Lake and town B be T. Now in the diagram given to you, measure these distances in centimeters. Let them be d, l and t respectively.
Now you have D/d = L/l = T/t. Solve this to get T. In this method you do not even have to calculate L. If no triangle is drawn only a map is given Make one triangle joining the three locations. Then the answer that you get would be approximate because the cars are not moving in straight lines.

Answer 3

If you have an angle to work with the problem can be solved quite easily because you know the length of 2 sides to the triangle and can use trig to find the last distance. or if you know which side is the hypotenuse you can use the equation A(squared) + B(squared)= C(squared), C being the hypotenuse. You must be missing something in the diagram, like an angle, or which path is longer.