Modeling with linear equations

Question

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 15 min. If the current in that part of the river is 9 km per hr, what was her boat speed in still water?

Answer 1

distance = rate x time

 

distance = (r - 9 ) * 1/2  <--- 30 min = 1/2 hour and speed is given in km per hour!

 

 distance = (r + 9) * 1/4 <--- 15 minutes = 1/4 hour going WITH the current downstream

 

(r-9)*1/2 = (r+9)*1/4

 

2*(r-9) = r + 9

 

2r - 18 = r + 9

 

2r - 18 - r - 9 = 0

 

r - 27 = 0

 

r = 27

 

the speed of the boat is 27 km per hour.

upstream, the boat goes 18 km per hour x 1/2 hour = 9 km.

downstream, the boat goes 36 km per hour x 1/4 hour = 9 km