find speed

Question

two station A & B are at 90km apart on a high way. a car start at A and another from B at same time with same speed. if they go in same direction then they meet after 9h. if they go in opposite direction then they meet after 1&2/7 h.

Answer 1

This is a simple set of two linear equations disguised as a word problem. Let's break it down as best as we can.

 

A = car A's speed

B = car B's speed

 

We will look at the two cars traveling in the same direction first. We know that they start 90 km apart and that they travel for 9 hours. We consider car A starting position to be 0, and car b starting position to be 90. This is represented by the equation:

 

9A = 9B + 90

We can say this because after traveling for 9 hours they end up at the same position and car B started ahead of car A so it gets the added 90 km.

 

Now for the cars traveling in opposite directions we have a similar setup.

 

(⁹/₇)A = 90 - (⁹/₇)B

The key here is the right side of the equation. We subtract (9/7)B because it is going in the opposite direction. That is to say, it starts at 90 and goes towards 0.

 

With these two equations set up the rest of the problem is a piece of cake, just a set of two linear equations.

 

Good Luck!