A motorboat travels 196 kilometers in 4 hours going upstream and 665 kilometers in 7 hours going downstream. what is the rate of the boat in still water and what is the rate of the current?

Question

Sowing a distance ,rate,time problem using a system of linear equation.

Answer 1

distance = rate of speed times time traveled

d=rt

r=d/t

r = 196/4 = 665/7

the system of equations are;

b+w = 665/7 and

b-w = 196/4 where w=the current speed of the water and b = the boat speed in still water

add to eliminate one variable

2b = 665/7 +196/4 = 95+49 = 144

2b = 144

divide by 2

b = 144/2 = 72 kmh = speed of the boat in still water

w = b-w = 72 - 49 = 23 kmh = water current speed

upstream the net speed was 72-23 = 49 kmh

49x4 = 196 km

downstream net speed was 72+23 = 95 kmh

95x7=665 km

the boat's speed in still water was 72 kilometers per hour

the current's speed was 23 kilometers per hour