Question

suppose cars now ""propagate"" at 1000 km/hr and suppose toll booth now takes one min to service a car q: will cars arrive to 2nd booth before all cars serviced at first booth

Answer 1

To determine if cars will arrive at the second booth before all cars are serviced at the first, we compare the travel time to the service time. Cars travel at 1000 km/hr or 16.67 km/min, so they would reach the second booth before being serviced at the first if the distance is less than 16.67 km.

Step-by-step explanation:

Assuming that the term 'propagate' is used synonymously with 'travel' in this context, we can solve the problem by calculating the time it would take for cars to arrive at the second booth after being serviced at the first. If cars travel at 1000 km/hr, and the toll booth services a car every minute, we can determine whether cars will arrive at the second booth before all cars are serviced at the first booth based on the distance between the booths.

Given that cars travel at 1000 km/hr, which is approximately 16.67 km/min, a car could potentially reach the second booth in 1 minute if the distance between the booths is less than or equal to 16.67 kilometers. Since the toll booth takes 1 minute to service each car, the answer depends on the distance between the booths. If the distance is less than 16.67 kilometers, then yes, cars would start arriving at the second booth before the first booth has serviced all the cars in the queue. If the distance is greater, cars will not reach the second booth before the servicing of all cars is complete at the first one.

Answer 2

The travel time between the booths (1.8 minutes) is shorter than the service time per car at the first booth (1 minute), indicating cars will reach the second booth while some cars are still being serviced at the first one.

How to solve

To determine whether cars will arrive at the second toll booth before all cars are serviced at the first booth, let's calculate the time it takes for a car to travel between the toll booths and compare it to the time taken to service cars at the first booth.

Given:

Car speed: 1000 km/hr

Service time at the first toll booth: 1 minute

Distance between the toll booths: 30 kilometers

First, let's convert the distance between the toll booths from kilometers to hours, considering the car's speed:

Time taken to travel between toll booths = Distance / Speed

Time taken to travel = 30 km / 1000 km/hr

Time taken to travel = 0.03 hours (or 1.8 minutes)

Comparing this time (1.8 minutes) to the time taken for the first toll booth to service a car (1 minute), it's evident that cars will arrive at the second toll booth before all cars are serviced at the first booth.

The travel time between the booths (1.8 minutes) is shorter than the service time per car at the first booth (1 minute), indicating cars will reach the second booth while some cars are still being serviced at the first one.

The Complete Question

Given a hypothetical scenario where cars travel at a speed of 1000 km/hr and a toll booth takes one minute to service a car, consider two consecutive toll booths situated 30 kilometers apart on a highway. Will the cars arrive at the second toll booth before all cars are serviced at the first booth?