A small motorboat travels 8 mph in still water. It takes 4 hours longer to travel 60 miles going upstream than it does going downstream. Find the rate of

WOW TOUGHT ONE WHAT GRADE ARE U IN

Le the rate of the current  = R

Rate with the current  = 8 + R

Rate against the current  = 8 - R

So....Distance / Rate  = Time   and we have that

The time it takes to go downstream + 4 hours   = time to go upstream   ...and we have....

60/ [8 + R]  + 4   =   60 / [8 - R ]     

4   =  60 / [8 - R]   -  60/ [8 + R ]     simplify the right side

4  =   (60[8 + R]   - 60[8 -R] )  / [  ( 8 + R) (8 -R) ]      cross-multiply

4 [  ( 8 + R) (8 -R) ]  =  480 + 60R - 480 + 60R

4 [ 64 - R^2]   =  120R      divide through by 4

64 - R^2  = 30R        rearrange

R^2 + 30R - 64   =  0

Factor

(R - 2) (r + 32)  = 0

Setting each factor to 0   we have that R =-32 mph   [reject ] or R = 2 mph

So....the current = 2 mph

Let the speed of the current =S

Let the time taken to travel with the current =T

T(8+S)=60, (T+4)(8-S) =60, solve for S, T

S =2 miles-the speed of the current

T=6 hours - time taken to travel with the current.