A boat traveled 36 km downstream in 2 h. return trip upstream=3 h. Find rate of current.

Question

This is mixed problem solving in chapter 6 of the Mcdougal Littel Algebra and Trig structure and method book 2.

Answer 1

Assume B = speed of the boat in still water

w = the speed of the water (or the rate of the river current)

Dd = distance gone down stream

Du = distance gone up stream

Td = time spent in going down stream

Tu = Time spent in gong upstream

D = rate * time

Dd = (B+W)Td

Du = (B-W)Tu

Boat traveled 36 km in 2h , then the equation is would be 36 = (B+W)2

B+W = 18

W = 18-B ---> (1)

Return trip distanceis same and in 3h , then the equation wouldbe 36 = (B-W)3

36 = 3B - 3W ---> (2)

From (1) substitute the W value.

36 = 3B - 3(18-B)

36 = 3B - 54 + 3B

36 + 54 = 6B

90 = 6B

B = 90/6

B = 15

Substitute the B value in equation (1).

W = 18-15 = 3

Rate of the cureent is 3mph.