How Long Does It Take for a Car to Catch Up to a Truck?

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To determine how long it takes for a car traveling at 90 km/h to catch up to a truck moving at 50 km/h, start by defining the position equations for both vehicles. The car's position can be expressed as P_car = 90t, while the truck's position, accounting for the initial 100m lead, is P_truck = 50t + 100. Setting these equations equal to each other allows for the calculation of time when both vehicles meet. Solving the equation 90t = 50t + 100 will yield the time required for the car to catch up. The final answer reveals the duration needed for the car to reach the truck.
muktl
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a car is going at 90 km/h

a truck is 50 km/h

the car is 100m behind the truck

so how long does the car need to reach to the truck?
 
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This should be in the homework help section. but first try writing an equation for the position of the car as a function of time and then write an equation for the position of the truck as a function of time plus 100m (this way the position of the truck is relative to the initial position of the car). Now, when they meet they meet at the same time and the same position so then simply equate the two equations to find the time.
 

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