Final answer:
The time ratio between the three cars with speeds 25 km/hr, 40 km/hr, and 60 km/hr to travel the same distance is 4.8 : 3 : 2.
Step-by-step explanation:
The ratio between the time taken by three cars to travel the same distance, with speeds of 25 km/hr, 40 km/hr, and 60 km/hr, can be found using the concept of inverse proportionality. Since speed and time are inversely proportional when distance is constant, we can use the formula Speed = Distance / Time to find the times taken by each car and then compute the ratio.
For the car with a speed of 25 km/hr to travel a certain distance, say d kilometers, the time taken (T1) would be T1 = d / 25 hours. Similarly, for the cars with speeds of 40 km/hr and 60 km/hr, the times taken would be T2 = d / 40 hours and T3 = d / 60 hours, respectively. To get the ratio, we don't need to know the actual distance d, as it will cancel out when we compute the ratio of times.
Thus, the time ratio of the cars is T1 : T2 : T3 = (d / 25) : (d / 40) : (d / 60). To simplify this ratio, multiply each term by the least common multiple of the denominators, which is 120, resulting in 120 / 25 : 120 / 40 : 120 / 60 = 4.8 : 3 : 2.