Finding speed of boat

Question

The speed of a river current is 2mph. If a boat travels 30 miles downstream in the same time that it takes to travel 20 miles upstream, find the speed of the boat in still water

Answer 1

Hi Angela,

 

Remember that distance/rate = time.

 

Distance = 30 miles downstream and 20 miles upstream

 

Time is equal in each direction

 

Rate in still water = X

 

Rate downstream = X + 2

 

Rate upstream = X -2

 

30/(X+2) = 20/(X-2)

 

Cross multiply--> 30(X-2) = 20(X+2)

 

30X - 60 = 20X + 40

 

10X = 100

 

X = 10

 

Check and see if the boat travels the same time if it goes downstream at 12 mph and upstream at 8 mph.

 

Have fun.

 

Dan