Ans. is 60 sec
in 45 sec car will travel
S=vt
S= 60×1000/3600×45=750 this is the min. distance between the cars
now if simultaneously their speeds get reduced so distance between them will remain same because simultaneously their speeds are changed and also their speeds are same.so
S=v*t*
750=45×1000/3600×t*
we get t*= 60sec

The Interval of Time Between Arrival of Cars at 2nd Town during Bad Conditions

To determine the interval of time between the arrival of cars at the 2nd town during bad conditions, we need to consider the initial interval between the cars and how the reduction in speed affects this interval.

Initial Interval:
- Initially, cars start at a regular interval of 45 seconds.
- This means that each car starts its journey towards the 2nd town 45 seconds after the previous car.

Effect of Speed Reduction:
- At some point in time, all the cars simultaneously reduce their speed from 60 km/h to 45 km/h due to bad conditions.
- This reduction in speed will affect the interval between the cars.

Calculating the New Interval:
- To calculate the new interval, we need to determine the time it takes for a car to travel the distance between the two towns at the reduced speed of 45 km/h.
- Let's assume that the distance between the two towns is D km.

Time to Travel at 60 km/h:
- At a speed of 60 km/h, a car can cover the distance D in the following time:
Time = Distance / Speed = D / 60

Time to Travel at 45 km/h:
- At a speed of 45 km/h, a car can cover the same distance D in the following time:
Time = Distance / Speed = D / 45

Change in Interval:
- The change in the interval between the cars is equal to the difference in time it takes for a car to travel the distance D at 60 km/h and 45 km/h.
- Let's denote the change in interval as Δt.

Calculating Δt:
- Δt = (D / 60) - (D / 45)
- Simplifying the equation, we get:
Δt = D * (1/60 - 1/45)
Δt = D * (3/180 - 4/180)
Δt = D * (-1/180)
Δt = -D/180

Interval of Time Between Arrival at 2nd Town:
- The interval of time between the arrival of cars at the 2nd town during bad conditions is the initial interval (45 seconds) plus the change in interval (Δt).

Calculating the Final Interval:
- Final Interval = Initial Interval + Δt
- Final Interval = 45 seconds + (-D/180)
- Final Interval = 45 - D/180 seconds

Explanation:
- The interval of time between the arrival of cars at the 2nd town during bad conditions depends on the distance between the two towns.
- As the distance increases, the interval between the cars also increases.
- This is because cars traveling at a reduced speed take longer to cover the same distance.
- The final interval is given by the initial interval (45 seconds) minus a fraction of the distance (D/180).
- The negative sign indicates that the interval between the cars increases as the distance increases.