a truck leaves point a traveling 6 mph. after two hours a car leaves point a traveling 90mph and follows the truck's route. at what distance from point a will the car catch the truck.
To find the distance from point A where the car catches the truck, we need to determine the time it takes for the car to catch up.
Let's assume the time taken by the car to catch up is 't' hours. After 2 hours, the truck has already been driving and covers a distance of 6 mph * 2 hours = 12 miles from point A.
During the time 't', both the truck and the car will cover the same distance.
Let's set up the equation using the formula: distance = rate × time:
For the truck: distance = 6t (since it started 2 hours earlier)
For the car: distance = 90t
Since they both cover the same distance when the car catches up to the truck, we can set up the equation:
6t = 90t
Now, let's solve for 't':
6t = 90t
Subtract 6t from both sides:
90t - 6t = 90t - 6t
84t = 0
Divide both sides by 84:
84t/84 = 0/84
t = 0
This means that the time it takes for the car to catch up to the truck is 0 hours. However, since the car does not catch up after 0 hours, it means that the car will never catch up to the truck.
Therefore, the car will never catch the truck, and the distance from point A where the car catches the truck is infinite.