Algebra 1 question in description

Question

A motorboat travels 123 kilometers in 3 hours going upstream. It travels 159 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

I am assuming that the current is moving downstream only.

Here is a picture

I am assuming that the motion UPSTEAM has no contribution of current

and the motion DOWNSTREAM is the sum of the motorboat motion AND the current.

DISTANCE( upstream ) = distance ( independent of current) = 123 km

rate of motorboat = 123 km/ 3 hr

time of upstream travel = 3 hr

DISTANCE( downstream) = 159 km

rate of motorboat = 123 km / 3 hr = 36 km/ hr

DISTANCE traveled due to current =

DISTANCE( downstream)) - DISTANCE due to rotor ( independent of currentl) =

159 km - 123 km = 36 km

|————motor——————————¡ upstream ( motor only)

| ———motor—————————— ¡——current—— downstream ( motor plus current)

the rate in still water = distance traveled due to motor/ time = 123 k m/ 3 hr = 41 km/ hr

the rate of the current = (distance traveled due to current)/ 3 hr = (distance traveled downstream - distance traveled upstream) / 3 hr = (159 km - 123 km = 36 km)/ 3 hr = 12 km/ hr

Answer 2

distance = rate x time

r = rate in still water; c = current

Going with current: 159 = 3(r + c) → 159 = 3r + 3c

Going upstream: 123 = 3(r - c) → 123 = 3r - 3c

Subtracting: 36 = 6c so c = 6 km/hr

Then 123 = 3r - 3(6) → 123 = 3r - 18

3r = 141 → r = 47 km/hr

Check: 3(47) + 3(6) = 141 + 18 = 159

3(47) - 3(6) = 141 - 18 = 123