SOLUTION: A motorboat travels 130 km in 5 hours going upstream. It travels 270 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rat

Question 997437: A motorboat travels 130 km in 5 hours going upstream. It travels 270 km 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?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39615) (Show Source): You can put this solution on YOUR website!
This form of question is so common, it will be solved here only symbolically.

KNOWN VARIABLES UNKNOWN VARIABLES VARIABLES' ASSIGMENTS speed time distance UPSTREAM r-c t n DOWNSTRM r+c t p

RT=D shows travel rates rule for uniform rate, relating rate time and distance.

, notice that terms are arranged so known coefficient on left
and unknown variable on the right, IN EACH TERM, in the left members.

Elimination Method can be used as a start.

Substitute the given assigned values to evaluate r and c.

Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!

A motorboat travels 130 km in 5 hours going upstream. It travels 270 km 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?

Let speed of boat, in still water be S, and speed of current, C
Then total upstream speed = S - C, and total downstream speed = S + C
We then get: ______S � C = 26 ------- eq (i)
_____S + C = 54 ------- eq (ii)
2S = 80 ------- Adding eqs (ii) & (i)
S, or speed of boat, in still water = , or km/h
40 + C = 54 --------- Substituting 40 for S in eq (ii)
C, or speed of current = 54 � 40, or km/h
RELATED QUESTIONS
A motorboat travels 145 km in 5 hours going upstream. It travels 205 going downstream in (answered by josmiceli)
A motorboat travels 198 km in 6 hours going upstream. It ravels 294 km going downstream... (answered by josgarithmetic)
A motorboat travels 268 km in 4 hours going upstream.It travels 420 km going downstream... (answered by stanbon)
A motorboat travels 225km in 5 hours going upstream. It travels 305km going downstream in (answered by Alan3354)
A motorboat travels 225 kilometers in 5 hours going upstream. It travels 395 kilometers... (answered by Boreal)
A motorboat travels145 mi in 5 hours going upstream. It travels 215 going downstream in (answered by josgarithmetic)
A motorboat travels 385 mi in 7 hours going upstream. It travels 623 mi going downstream... (answered by oberobic)
A motorboat travels in hours going upstream. It travels going downstream in the same... (answered by checkley79)
A motorboat travels in hours going upstream. It travels going downstream in the same... (answered by Alan3354)