word problem

Question

Point A and B are seperated by a distance of 280 KM. If two cars left each point at the same time traeling towards each other, they would meet in 2 hours. If two cars left each point at the same time moving in the same direction, the car that left point A would catch up with the car that left point B in 14 hours. What is the speed of both cars?

Answer 1

OK, Sam, d = rt, right?

 

The first equation, the total distance is 280 km. If a = the rate of car one and b = the rate of car 2,

 

2a + 2b = 280

 

Now, in the 2nd scenario, car 2 goes a certain distance, but car 1 goes the entire 280 km plus the extra distance to catch up.

 

14a = 280 + 14b

 

Now, "solve" the first equation for a.

 

2a = 280 - 2b

a = 140 - b

 

Then substitute this "value" for a into the 2nd equation.

 

14(140 - b) = 280 + 14b

 

Solve for b, take what you get and substitute it into the first equation to solve for a.

 

Hope this helps!