Lucy takes 5.5 hours to travel between 2 cities that are 250 km apart. She travels two fifths of the distance at a rate of 90 km/hr on a highway. She drives the rest of the distance on local roads. What is her average speed for the second part of her journey?
distance 1st part ... 2/5 * 250 km
travel time 1st part ... (2/5 * 250 km) / 90 kph
distance 2nd part ... 250 km minus distance 1st part
time 2nd part ... 5.5 hr minus time 1st part
average speed 2nd part ... distance 2nd part divided by time 2nd part
To find Lucy's average speed for the second part of her journey, we need to calculate the time it takes for her to travel on local roads.
We know that Lucy travels two-fifths of the distance (250 km) on the highway, which is equal to (2/5) * 250 = 100 km.
Since we know her speed on the highway is 90 km/hr, we can calculate the time it takes for her to travel this distance by dividing the distance by the speed:
Time on highway = Distance / Speed = 100 km / 90 km/hr = 1.11 hours (approximately)
Now, to find the time Lucy takes to travel on local roads, we subtract the time spent on the highway from the total travel time of 5.5 hours:
Time on local roads = Total travel time - Time on highway = 5.5 hours - 1.11 hours = 4.39 hours (approximately)
Finally, we can calculate Lucy's average speed on local roads by dividing the distance traveled on local roads (150 km) by the time taken:
Average speed on local roads = Distance on local roads / Time on local roads = 150 km / 4.39 hours ≈ 34.15 km/hr
Therefore, Lucy's average speed for the second part of her journey is approximately 34.15 km/hr.