Two cars 288 km apart start at the same time moving towards each other and meet after 12 hours. If the speed of 1 car is 5 km\h faster than the other car, find the speed of each car.
speed of slower car --- x km/h
speed of faster car ---- x+5 km/h
When they meet, each will have gone for 12 hrs
12x + 12(x+5) = 288
24x = 228
x = 9.5
slow car went 9.5 km/h, the faster went 14.5 km/h
check:
12(9.5) + 12(14.5) = 288 , the answers are correct mathematically
A poorly designed question, the answers are not realistic
To find the speed of each car, we can use the concept of relative speed.
Let the speed of one car be 'x' km/h. The other car's speed is then 'x+5' km/h.
The distance traveled by both cars will add up to the total distance of 288 km.
Since they are moving towards each other, the combined speed is the sum of their speeds.
So, the equation for the total distance can be written as:
Distance = Speed × Time
Therefore, for the first car with speed 'x' km/h, the distance it covers is:
Distance1 = x km/h * 12 hours = 12x km
Similarly, for the second car with speed 'x+5' km/h, the distance it covers is:
Distance2 = (x + 5) km/h * 12 hours = 12(x + 5) km
Since they meet after 12 hours, the sum of the distances covered by both cars should be equal to the total distance:
Distance1 + Distance2 = Total Distance
12x + 12(x + 5) = 288
Now we can solve this equation to find the value of 'x', which represents the speed of the first car.
12x + 12x + 60 = 288
24x = 228
x = 9.5
So, the speed of the first car is 9.5 km/h, and the speed of the second car is 9.5 + 5 = 14.5 km/h.