Traveling equation

Question

A grain barge travels on a river from point A to point B loading and unloading grain. The barge travels at a rate of 10 mph relative to the water. The river flows downstream at a rate of 1 mph. If the trip upstream takes 2 hours longer than the trip​ downstream, how far is it from point A to point​ B?

Answer 1

upstream takes 2 hours longer than downstream

current = 1 mph

barge goes 10 mph relative to the water

distance = time times speed

AB = BA, same distance both ways, t = time downstream, t+2 = time upstream

(10+1) = speed down stream, 10-1 = speed upstream

distance downstream= distance upstream

t(10+1) = (t+2)(10-1)

11t = 9t +18

2t = 18

t=18/2

t = 9 hours downstream, t+2= 9+2 = 11 hours upstream

9(10+1) = 11(10-1) = 9(11) = 99 miles from A to B