Final answer:
To find how long the journey takes at 45 km/h, the time can be calculated by dividing the distance (30 km) by the new speed (45 km/h), which results in 2/3 hours or 40 minutes.
Step-by-step explanation:
If a journey takes 1/2 hour at an average speed of 60 km/h, then the total distance covered in the journey can be calculated using the formula distance = speed × time. In this case, the distance would be 60 km/h × 0.5 h = 30 km. To find how long it takes at 45 km/h, the same distance is used, and the time can be calculated by rearranging the formula to time = distance ∕ speed, which would be 30 km ∕ 45 km/h.
Upon performing this calculation, the time it takes at 45 km/h would be 2/3 hours or 40 minutes, as the new speed is 3/4 of the original speed, thus the time will take 4/3 times as long.
It is important to carry out a sanity check to ensure that our answers are reasonable given the information from the problem. As speed decreases, time should increase proportionally, and since 45 km/h is three quarters of 60 km/h, it makes sense that the journey would take one third longer than half an hour, which corresponds to 2/3 hours or 40 minutes.