Find meeting time, given distance, and cycling rates.

[sandyk109]

At 9:30 a.m. Andrew left Exter for Portsmouth, cycling at 12 mi/h. At 10:00 a.m. Stacy left Portsmouth for Exetr, cycling at 16 mi/h. The distance from Exeter to Portsmouth is 20 mi. Find the time when they met.

 

[skeeter]

let t = time measured starting at 10:00 am when they meet

sum of the distance that both travel = 20

since rate*time = distance ...

16t + 12(t + .5) = 20

solve for t, then add the result to 10:00 am to find the time they meet.

 

[Denis]

Sandy, this is another (quicker) way to "get" answer:

when Stacy leaves, Andy has travelled 6 miles (1/2 hour @ 12 mph);
so distance left at that point = 20 - 6 = 14 miles;
this 14 miles is covered at combined speed of 12 + 16 = 28 mph;
so time to cover that = 14 / 28 = 1/2 hour;
so time of meeting = 10 + 1/2 = 10:30.