The distance between District One and District Twenty was 290 km. Ashley left District One at 10 30 and travelled at an average speed of 80 km/h towards District Twenty. An hour later, Aaron left District Twenty and travelled to District One using the same route. Aaron's average speed was 60 km/h. At what time did they pass each other?
Question
The distance between District One and District Twenty was 290 km. Ashley left District One at 10 30 and travelled at an average speed of 80 km/h towards District Twenty. An hour later, Aaron left District Twenty and travelled to District One using the same route. Aaron's average speed was 60 km/h. At what time did they pass each other?
Solution
Step 1: Calculate how far Ashley travelled before Aaron started his journey.
Ashley started her journey an hour before Aaron, so she had already travelled for an hour at an average speed of 80 km/h.
Distance = Speed x Time Distance = 80 km/h x 1 hour = 80 km
Step 2: Calculate the remaining distance between Ashley and Aaron.
The total distance between District One and District Twenty is 290 km. Ashley had already travelled 80 km, so the remaining distance is 290 km - 80 km = 210 km.
Step 3: Calculate when Ashley and Aaron will meet.
They are now moving towards each other, so their combined speed is 80 km/h + 60 km/h = 140 km/h.
To find out when they will meet, we divide the remaining distance by their combined speed.
Time = Distance / Speed Time = 210 km / 140 km/h = 1.5 hours
Step 4: Calculate the actual time they meet.
Ashley started her journey at 10:30. She travelled for an hour before Aaron started, and then they travelled for another 1.5 hours before they met.
So, they met 1 hour + 1.5 hours = 2.5 hours after Ashley started her journey.
2.5 hours after 10:30 is 13:00, or 1:00 PM.
So, Ashley and Aaron passed each other at 1:00 PM.
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