At 11 a.m., a car travelled from Town X to Town Y at 80 km/h. At the same time, a lorry travelled from Town Y to Town X at 55 km/h. After traveling for 2 1/2 h, they were still some distance apart. Both vehicles travelled for another 2 h before they met each other.
(a) What was the distance between both vehicles after 2 1/2 h?
(b) What was the distance between Town X and Town Y?
(a) After traveling for 2 1/2 hours, the car would have covered a distance of 80 km/h * 2.5 h = <<80*2.5=200>>200 km.
At the same time, the lorry would have covered a distance of 55 km/h * 2.5 h = <<55*2.5=137.5>>137.5 km.
Therefore, the distance between both vehicles after 2 1/2 hours is 200 km + 137.5 km = <<200+137.5=337.5>>337.5 km.
(b) After meeting each other, both vehicles traveled for another 2 hours before they met.
During this time, the car would have covered a distance of 80 km/h * 2 h = <<80*2=160>>160 km.
At the same time, the lorry would have covered a distance of 55 km/h * 2 h = <<55*2=110>>110 km.
Therefore, the total distance between Town X and Town Y is 337.5 km + 160 km + 110 km = <<337.5+160+110=607.5>>607.5 km. Answer: \boxed{607.5}.
To find the distance between the two vehicles after 2 1/2 hours, we can calculate the distance each vehicle traveled in that time.
The car traveled at a speed of 80 km/h for 2 1/2 hours, so the distance it traveled can be calculated as follows:
Distance Car Traveled = Speed × Time
= 80 km/h × 2.5 h
= 200 km
Similarly, the lorry traveled at a speed of 55 km/h for 2 1/2 hours, so the distance it traveled can be calculated as follows:
Distance Lorry Traveled = Speed × Time
= 55 km/h × 2.5 h
= 137.5 km
Therefore, after 2 1/2 hours, the car and lorry were some distance apart. The distance between them was the difference between the distances each vehicle traveled:
Distance Apart = Distance Car Traveled - Distance Lorry Traveled
= 200 km - 137.5 km
= 62.5 km
Therefore, the distance between both vehicles after 2 1/2 hours was 62.5 km.
To find the distance between Town X and Town Y, we need to calculate the total distance both vehicles traveled before they met.
We know that after the initial 2 1/2 hours, both vehicles continued to travel for an additional 2 hours until they met each other.
The car traveled at a speed of 80 km/h for a total of 2 1/2 hours + 2 hours, so the total distance it traveled can be calculated as follows:
Total Distance Car Traveled = Speed × Total Time
= 80 km/h × (2.5 h + 2 h)
= 80 km/h × 4.5 h
= 360 km
Similarly, the lorry traveled at a speed of 55 km/h for the same total time, so the total distance it traveled can be calculated as follows:
Total Distance Lorry Traveled = Speed × Total Time
= 55 km/h × (2.5 h + 2 h)
= 55 km/h × 4.5 h
= 247.5 km
Therefore, the total distance between Town X and Town Y can be calculated as the sum of the distances each vehicle traveled:
Total Distance = Total Distance Car Traveled + Total Distance Lorry Traveled
= 360 km + 247.5 km
= 607.5 km
Therefore, the distance between Town X and Town Y is 607.5 km.