SOLUTION: Kate can row a boat 10 miles per hour in still water. In a river where the current is 5 miles per hour, it takes her 4 hours longer to row a given distance upstream than to travel

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Kate can row a boat 10 miles per hour in still water. In a river where the current is 5 miles per hour, it takes her 4 hours longer to row a given distance upstream than to travel       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1002733: Kate can row a boat 10 miles per hour in still water. In a river where the current is 5 miles per hour, it takes her 4 hours longer to row a given distance upstream than to travel the same distance downstream. Find how long it takes her to row upstream, how long to row downstream, and how many miles does the row one way
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
            rate          time      distance
UPST        10-5=5        t+4         d
DOWN        10+5=15        t          d

RT=D basic uniform travel rates rule

5%28t%2B4%29=15t because distance is d both directions.
5t%2B20=15t
20=10t
highlight%28t=2%29

Going upstream, 2 hours
Going downstream, 6 hours

You can find d.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Kate can row a boat 10 miles per hour in still water. In a river where the current is 5 miles per hour, it takes her 4 hours longer to row a given distance upstream than to travel the same distance downstream. Find how long it takes her to row upstream, how long to row downstream, and how many miles does the row one way
Let distance be D

Then time taken to row upstream is: D%2F%2810+-+5%29, or D%2F5

Time taken to row downstream is: D%2F%2810+%2B+5%29, or D%2F15

Since upstream time takes 4 hours longer than downstream time, then we get:

D%2F5+-+4+=+D%2F15

3D – 60 = D ------- Multiplying by LCD, 15

3D – D = 60

2D = 60

D, or distance = 60%2F2, or highlight_green%2830%29 miles

Time taken to row upstream: D%2F5, or 30%2F5, or highlight_green%286%29 hours

Time taken to row downstream: D%2F15, or 30%2F15, or highlight_green%282%29 hours