How do you work this word problem?

In his boat carl takes 1.5 times as long to go 72 miles upstream as he does to make the return trip downstream. If the boat cruises at 30 mph in still water, what is the speed of the current.How do you work this word problem?
Downstream:


rate = 30 + c


distance = 72


time = distance / rate = 72 / (30 + c)





Upstream:


rate = 30 - c


distance = 72


time = 72 / (30 - c)





So, solve:


1.5 * time downstream = time upstream


(1.5)(72) / (30 + c) = 72 / (30 - c)


(1.5)(72)(30 - c) = (72)(30 + c)


(1.5)(30 - c) = 30 + c


45 - 1.5c = 30 + c


15 = 2.5c


6 = c





So the speed of the current is 6 mphHow do you work this word problem?
You basically have two rate problems:





Distance = rate * time





72 miles = rate1 * time1





72 miles = rate2 * time2





rate1 = 30 - current





rate2 = 30 + current





time1 = 1.5 * time2





Now, substitute the rates and the times in the first two equations, and solve for the current.
time down stream = t


time up stream = 1.5t


speed at still water, v = 30mph


current speed, c = ?


distance, s traveled upstream = (speed)(time)= 72 miles


equals distance travelled down stream





s downstream = (30 +c)t = 72


s upstream = (30 - c)1.5t = 72





t = 72/(30 + c) ; t = 72/(30 - c)(1.5)





equate t





(30 - c)(1.5) = 30 + c


45 - 1.5c = 30 + c


15 = 2.5c


c = 6 mph = speed of current