Solving a distance, rate, time problem using a rational equation

Question

Ivan's boat has a top speed of 9 miles per hour in still water. While traveling on a river at top speed, he went 10 miles upstream in the same amount of time he went 20 miles downstream. Find the rate of the river current.

Answer 1

Stephanie, no one has answered you yet...  Here's my best explanation:

 

10 miles  (1 hr/9miles - c ) = 20 miles  (1 hr/ 9 miles + c)

 

c is the current

 

10/(9m - c) = 20/(9m + c)

 

Multiply both sides by (9m + c)(9m - c)

 

10(9m + c) = 20 (9m - c)

 

Divide by 10

 

9m + c = 18m - 2c

 

3 c = 9m

 

c = 3 mph

 

Check: 

 

(1hr/12 miles)(20 miles) = 5/3 hr

 

(1hr/6 miles)(10 miles) = 5/3 hr

 

I hope you can follow this...