Question 137672
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Let r=speed of the current
tugboat's speed upstream=10-r
tugboat's speed downstream=10+r

Time for tugboat to travel upstream=24/(10-r)
Time for tugboat to travel downstream=24/(10+r)

Now we are told that the sum of the above two times equals 5 hours, so our equation to solve is:

24/(10-r)+24/(10+r)=5  multiply each term by (10-r)(10+r)

24(10+r)+24(10-r)=5(10-r)(10+r)  get rid of parens

240+24r+240-24r=500-5r^2  subtract 500 from and add 5r^2 to both sides

240+24r+240-24r-500+5r^2=500-500-5r^2+5r^2  collect like terms

-20+5r^2=0 rearranging:
5r^2-20=0  divide each side by 5
r^2-4=0-------------------------------quadratic in standard form and it can be factored

(r-2)(r+2)=0
r=2 mph--------------------speed of the current
and
r=-2 mph----------------------DISREGARD--- CURRENT SPEED IS POSITIVE

ck
24/(10-2)+24/(10+2)=5
3+2=5
5=5


Hope this helps----ptaylor