Problema Solution
Two cars leave simultaneously from points A and B, the distance between which is 280 km. If the cars move to meet each other, they’ll meet in 2 hours. But if they move in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours. What is the speed of each of the cars?
Answer provided by our tutors
Let
v1 = the speed of the first car
v2 = the speed of the second car
t1 = 2 hr the time they need to meet while moving towards each other
t2 = 14 hr the time the car from point A needs to catch up with the car from point B while moving in same direction
d = 280 km the distance between A and B
Using the formula distance = speed*time when traveling towards each other we have:
v1t1 + v2t2 = d
2v1 + 2v2 = 280 divide both sides by 2
v1 + v2 = 140
When moving in the same direction we have:
v1t2 = v2t2 + d
14v1 = 14v2 + 280 divide both sides by 14
v1 = v2 + 20
We have the following system of equations:
v1 + v2 = 140
v1 = v2 + 20
........
click here to see the system of equations solved for v1 and v2
........
v1 = 80 km/hr
v2 = 60 km/hr
The speed of the car from point A is 80 km/hr while the speed of the car from point B is 60 km/hr.