Swim Upstream & Downstream
Calculate the time it takes swimmer #1 with speed s (wrt water) to go a distance w downstream and w upstream if the speed of the water is v (wrt bank).
- Downstream:
- What is swimmer’s speed (wrt bank)? vD = s + v
- How long does it take to go distance w? tD = w/vD = w/(s+v)
- Upstream:
- What is swimmer’s speed (wrt bank)? vU = s - v
- How long does it take to go distance w? tU = w/vU = w/(s-v)
- Total Time:
- Add the times tD and tU: T1 = w/(s+v) + w/(s-v)
- After some algebra, we can rewrite
in a more compact form: T1 = ?2 (2w/s)
where
? = 1 / sqrt(1 - (v/ s) 2)