Physics help -vectors please?

Question

need help

A swimmer is training in a river. The current flows at 1.62 metres per second and the swimmer swims upstream a distance of 151 metres before swimming back to the starting point. If the total time for the swim is 189.0 seconds, what is the swimmer's speed relative to the water?

Give your answer in metres per second (m/s) and round it to two decimal places.

Swimmer's Speed (m/s) =

Answer 1

Let:

u m/sec. be the swimmer's speed relative to the water,

t sec. be the time to swim upstream.

The time to swim downstream is 189 - t sec.

Upstream:

151 = (u - 1.62)t

t = 151 / (u - 1.62) ...(1)

Downstream:

151 = (u + 1.62)(189 - t)

Substituting for t from (1):

151 = (u + 1.62) [189 - 151 / (u - 1.62) ]

151(u - 1.62) = (u + 1.62)[ 189(u -1.62) - 151 ]

151u - 244.62 = (u + 1.62)(189u - 457.18)

= 189u^2 - 151u - 740.6316

189u^2 - 302u - 496.0116 = 0

Discarding the negative root:

u = (302 + sqrt[ 302^2 + 4 * 189 * 496.0116 ] ) / (2 * 189)

u = 2.61 m/s.