A car traveling 95 km/h is 210 m behind a truck traveling 75 km/h. How long will it take the car to reach the truck?

Question

Layla Ahmed · Accepted Answer

#t = "0.0084 hr"# or #"0.504 min"# or #"30.24 s"#

Compose the distance in relation to time.

#x_"car" = 95t - 0.210#

#x_"truck" = 75t #

You need

#x_"car" = x_"truck"#

When the car gets to the truck, the two distance functions are equal.

#95t - 0.210 = 75t #

#95t - 75t = 0.210#

#25t = 0.210#

#t = 0.210/25 #

#t= "0.0084 hr = 0.504 min = 30.24 s"#

Layla Ahmed · Answer

undefined To calculate the time it will take for the car to reach the truck, we first need to determine the relative speed between the two vehicles. Since the car is traveling faster than the truck, the relative speed is the difference between their speeds, which is 95 km/h - 75 km/h = 20 km/h.

Next, we convert the relative speed to meters per second (m/s) by multiplying by 1000/3600 (since 1 km/h is equal to 1000 m/3600 s). So, the relative speed is 20 km/h * 1000 m/3600 s ≈ 5.56 m/s.

The distance the car needs to cover to reach the truck is 210 meters. To find the time it will take, we use the formula: time = distance / speed.

So, the time it will take for the car to reach the truck is 210 m / 5.56 m/s ≈ 37.67 seconds.