Truck A leaves a truck stop traveling at 80 km/hr. Four hours later, truck BB leaves the same truck stop traveling in the same direction at 90 km/ hr. How long does it take truck B to catch up to truck A?
let the time traveled by truck A be t hours, then A went 80t km
clearly the time traveled by truck B must be t-4 hours,
Didn't he then go 90(t-4) km
Now I wonder how far each of them went, ...
mmmmhhh?
The distance they travel is the same, and the time is 4 hours different.
DistanceA=80*time
DistanceB=90*(time-4)
set them equal, and solve for time. That is the total time, if you want the time B was traveling, subtract four hours.
To find out how long it takes for truck B to catch up to truck A, we need to determine the time it takes for truck B to cover the same distance (catch up) as truck A.
Let's start by finding out how far truck A travels in the time it takes for truck B to catch up. We know that truck A travels at a constant speed of 80 km/hr. The time it takes for truck B to catch up is the time it takes for truck A to travel that distance.
Distance = Speed × Time
Let's assign a variable for the time it takes for truck B to catch up to truck A. We'll call it T.
Now let's calculate how far truck A travels in time T:
DistanceA = SpeedA × TimeA
DistanceA = 80 km/hr × T
Since truck A has a head start of 4 hours, the time it takes truck A to travel the distance of T is T + 4 hours.
DistanceA = 80 km/hr × (T + 4)
Now we can calculate the distance truck B travels to catch up to truck A. Truck B travels at a speed of 90 km/hr for a time of T hours.
DistanceB = SpeedB × TimeB
DistanceB = 90 km/hr × T
For truck B to catch up to truck A, the distances they both travel need to be equal. So we equate the two distance equations:
DistanceA = DistanceB
80 km/hr × (T + 4) = 90 km/hr × T
Now we can solve this equation to find the value of T, which represents the time it takes for truck B to catch up to truck A.
80T + 320 = 90T
Rearranging the equation, we get:
10T = 320
Dividing both sides of the equation by 10, we find:
T = 32
Therefore, it takes truck B (or truck BB) 32 hours to catch up to truck A (or truck A).