Question

Jim is driving his car at 32 m/s (72 mi/h) along a highway where the speed limit is 25 m/s (55 mi/h). A highway patrol car observes him pass and quickly reaches a speed of 35 m/s. At that point, Jim is 350 m ahead of the patrol car. How far does the police car travel before catching Jim?

Answer 1

The police car will travel 4083.45 meters before catching Jim by using the relative speed to calculate the time taken to close the distance and then determining the total distance covered by the police car.

Step-by-step explanation:

To calculate how far the police car will travel before catching Jim, we need to consider the relative speed between Jim's car and the police car. Jim travels at 32 m/s and the police car travels at 35 m/s. The relative speed between the two is the speed of the police car minus the speed of Jim's car: 35 m/s - 32 m/s = 3 m/s.

The distance Jim is ahead of the police car is 350 m. The time it will take for the police car to catch Jim can be found by dividing the distance by the relative speed: time = distance / relative speed = 350 m / 3 m/s = 116.67 seconds.

Now, we can find how far the police car travels during this time by multiplying its speed by the time it took to catch up: distance traveled by police car = speed of police car × time = 35 m/s × 116.67 s = 4083.45 m. Therefore, the police car will travel 4083.45 meters before catching Jim.

Answer 2

The police car travel before catching Jim is 4.08 km.

Step-by-step explanation:

Given that,

Distance = 350 m

Speed of car = 32 m/s

Speed of petrol car = 35 m/s

Patrol car covered the distance is 350+x with the speed of 35 m/s.

Car covered the distance is x with the speed of 32 m/s.

We need to calculate the time for patrol car

`t=(35)/(350+x)`

We need to calculate the time for car

`t=(32)/(x)`

The time of both car is same.

`(35)/(350+x)=(32)/(x)`

`x = (350*32)/(3)`

`x=3733.33\ m`

We need to calculate the police car travel before catching Jim

`x'=x+350`

`x'=3733.33+350`

`x'=4083.33\ m`

`x'=4.08\ km`

Hence, The police car travel before catching Jim is 4.08 km.