Question

A motorboat travels 392 kilometers in 7 hours going upstream and 384 kilometers in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?rate of the boat in still water ___rate of the current:____

Answer 1

B= speed of the boat in still water

C = speed of the stream

speed upstream = B-C

Speed downstream = B+C

distance = Rate x time

upstream

392 = (B-C) 7

Downstream

384 = (B+C) 4

Solve the system of equations:

392 = 7B-7C (a)

384 = 4B + 4C (b)

Solve (a) for B:

392+7c = 7B

(392+7c) /7 = B

B = 56+c

Replace the value of B on equation (b) and solve for c

384 = 4 (56 +c) + 4c

384 = 224 + 4c +4c

384-224 = 4c+4c

160 = 8c

160/8 = c

20 = c

Replace c on (a)

392= 7B -7 (20)

392 = 7B -140

392+140 = 7B

532= 7b

B = 532/7

B= 76

c= 20

B= 76