SOLUTION: Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 1o min. If the current in that part of
Algebra.Com
Question 455185: Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 1o min. If the current in that part of the river is 3 km per hour, what was her boat speed in still water?
Can someone show me the set up for this?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 1o min. If the current in that part of the river is 3 km per hour, what was her boat speed in still water?
Can someone show me the set up for this?
---------------------
Upstream DATA:
time = 1/2 hr ; distance = x km ; rate = d/t = x/(1/2) = (2x) km/h
-------------------
Downstream DATA:
time = 1/6 hr ; distance = x km ; rate = d/t = x/(1/6) = (6x) km/h
-----------------------
Upstream rate = b-3 km/h where b is the speed of the boat in still water
Downstream rate b+3 km/h
-----
Solve this system of equations:
rate = rate:
b-3 = (2x)
b+3 = (6x)
----
Subtract and solve for "x":
6 = 4x
----
x = 3/2 km
-----
Solve for "b":
b -3 = 2x
b -3 = 2(3/2)
b -3 = 3
b = 6 km/h (speed of the boat in still water)
================================================
===========
A shorter way to work the problem.
Let b+3 be downstream rate.
and b-3 be upstream rate.
---------------------------
Distance up = Distance down = (rate)(time)
(b+3)(1/6 hr) = (b-3)(1/2 hr)
---
Multiply both sides by 12 to get:
2b+6 = 6b-18
4b = 24
b = 6 km/hr (speed of the boat in still water)
================
Cheers,
Stan H.
RELATED QUESTIONS
Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming... (answered by josmiceli)
Jane took 30 min to drive her boat upstream to water-ski at her favorite spot.... (answered by mananth)
Jane took 15 min to drive her boat upstream to water-ski at her favorite spot. Coming... (answered by jorel1380,josmiceli,MathTherapy)
Jane took
15 min to drive her boat upstream to water-ski at her favorite spot. (answered by josgarithmetic,josmiceli,MathTherapy,greenestamps)
Joanna took 30 min. to drive her boat upstream to water-ski at her favorite spot. Coming... (answered by ptaylor)
Jane took 10 minutes to drive her boat upstream to water ski at her favorite spot. Coming (answered by richwmiller)
Jane took 30min to drive her boat upstream to water-ski at her favorite spot. Coming back (answered by jorel555)
JOan took 20 min to drive her boat upstream to water ski at her favorite spot. Coming... (answered by checkley75)
Callie took 20 min to drive her boat upstream to water ski at her favorite spot. Coming... (answered by ewatrrr)