Final answer:
Your friend will need to travel for approximately 1.17 hours or 70 minutes before you are 125 km apart, since you have a 30-minute head start and you're both traveling in opposite directions at speeds of 40 km/h and 50 km/h respectively.
Step-by-step explanation:
To determine the number of hours your friend needs to travel before you are 125 km apart, we can use the concept of relative speed. Since you are traveling in opposite directions, we add your speed and your friend's speed to get the relative speed. The formula for calculating the distance based on speed and time is: Distance = Speed × Time. You traveled west at 40 km/h and your friend traveled east at 50 km/h. Therefore, the relative speed is 40 km/h + 50 km/h = 90 km/h.
Since you had a 30-minute head start, you would have already traveled 40 km/h × 0.5 h = 20 km. Now, the remaining distance to be covered to be 125 km apart would be 125 km - 20 km = 105 km.
Your friend would then need to travel 105 km at a speed of 90 km/h. The time taken can be calculated using the formula: Time = Distance / Speed, which is Time = 105 km / 90 km/h = 1.17 hours, or approximately 70 minutes.