At 9:30 A.M. Andrew left Exeter for Portsmouth, cycling at 12 miles per hour At 10:00 A.M. Stacy left Portsmouth for Exeter, cycling at 16 miles pewr hour. The distance from Exeter to Portsmouth is 20 miles. At what time did they meet?
When they meet, they will have travelled a combined distance of 20 miles. Let t be the time (in hours)after Andrew starts at 9:30.
12 t + 16 (t-0.5) = 20
28 t -8 = 20
28 t = 28
t = 1 hour
To find out when Andrew and Stacy meet, we need to determine the time it takes for each of them to travel.
Let's start with Andrew:
Speed = 12 miles/hour
Distance = 20 miles
Time = Distance / Speed
Time = 20 miles / 12 miles/hour = 1.67 hours
Andrew started at 9:30 A.M., so he would have reached the meeting point at:
9:30 A.M. + 1.67 hours = 11:17 A.M. (rounded to the nearest minute)
Now, let's calculate Stacy's time of arrival:
Speed = 16 miles/hour
Distance = 20 miles
Time = Distance / Speed
Time = 20 miles / 16 miles/hour = 1.25 hours
Stacy started at 10:00 A.M., so she would have reached the meeting point at:
10:00 A.M. + 1.25 hours = 11:15 A.M. (rounded to the nearest minute)
Therefore, Andrew and Stacy would have met at 11:15 A.M.
To find the time when Andrew and Stacy meet, we can use the concept of relative speed.
Let's consider the time it takes for Andrew to cycle from Exeter to the meeting point as T hours. During this time, he covers a distance of 12T miles.
Similarly, let's consider the time it takes for Stacy to cycle from Portsmouth to the meeting point as T - 0.5 hours. The reason we subtract 0.5 hours is because Stacy started 30 minutes (0.5 hours) later than Andrew. During this time, she covers a distance of 16(T - 0.5) miles.
Since the total distance between Exeter and Portsmouth is 20 miles, we can write the equation:
12T + 16(T - 0.5) = 20
Simplifying the equation:
12T + 16T - 8 = 20
28T = 28
T = 1
Therefore, T = 1 hour, which means Andrew and Stacy meet after 1 hour.
Andrew started at 9:30 A.M., so the meeting time would be 9:30 A.M. + 1 hour = 10:30 A.M.
Therefore, Andrew and Stacy meet at 10:30 A.M.