Final answer:
The friend needs to travel for 1.5 hours (Option A) before they are 125 km apart from the student, considering the distances and speeds provided.
Step-by-step explanation:
The student traveled west at an average speed of 40 km/h, and their friend traveled east at an average speed of 50 km/h 30 minutes later. To find out how long it will take the friend to travel before they are 125 km apart, we need to account for the distance the student has already traveled by the time the friend starts their journey. Since the student had a 30-minute head start, we calculate the distance the student traveled in that time:
- Distance = Speed × Time
- Distance = 40 km/h × 0.5 hours = 20 km
Now, when the friend begins traveling, the student and the friend are effectively moving apart at a combined speed of 40 km/h + 50 km/h = 90 km/h. The student is already 20 km away, so there is 105 km left to cover to reach 125 km apart:
- Time = Distance / Speed
- Time = 105 km / 90 km/h = 1.17 hours
Therefore, the friend needs to travel for 1.17 hours, which is roughly 1 hour and 10 minutes. However, since the options provided in the question are in half-hour increments and we need to round to the nearest option, the answer is: