anonymous
  • anonymous
A boat travels at a rate of 15km/hr in still water . It travels 60km upstream in the same time that it travels 90km downstream. What is the rate of the current ?
Algebra
katieb
  • katieb
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mathstudent55
  • mathstudent55
Current speed = c Boat speed is still water = s Boat speed upstream = s - c Boat speed downstream = s + c
mathstudent55
  • mathstudent55
speed = distance/time
mathstudent55
  • mathstudent55
distance = speed * time

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mathstudent55
  • mathstudent55
You understand the table so far? |dw:1435634606883:dw|
anonymous
  • anonymous
Mk but we don't know the time
anonymous
  • anonymous
Ya I get the table
mathstudent55
  • mathstudent55
|dw:1435634823006:dw|
mathstudent55
  • mathstudent55
Using: distance = speed * time you get this system of equations: 60 = (15 - c)t 90 = (15 + c)t
mathstudent55
  • mathstudent55
We solve both equation for t and set them equal to each other: \(t = \dfrac{60}{15 - c} \) \(t = \dfrac{90}{15 + c} \)
mathstudent55
  • mathstudent55
\(\dfrac{60}{15 - c} = \dfrac{90}{15 + c} \)
mathstudent55
  • mathstudent55
Cross multiply: 90(15 - c) = 60(15 + c) Divide both sides by 10: 9(15 - c) = 6(15 + c) 135 - 9c = 90 + 6c -15c = -45 c = 3
mathstudent55
  • mathstudent55
The current is 3 km/h
anonymous
  • anonymous
Okay I understand it I have 3 more problems like this but can u tell me if I am doing it right ?

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