Word problem?! helpme

A grain barge travels down a river from point A to point B loading and unloading grain. The barge travels at a rate of 12 miles per hour relative to the water. The water flows downstream at a a rate of 1mph. if the trip upstream takes 2 hours longer then the trip downstream, How far is it from point A to point B?

Downstream speed is 12 + 1 or 13 mph. Its upstream speed is 12 - 1 or 11 mph.

Distance is rate times time. Use D for the distance and T for the downstream time. Two hours longer going upstream is T + 2.

Downstream:

D = 13T

Upstream:

D = 11(T + 2)

Since the distance is the same, you can equate the two right sides and solve for T:

13T = 11(T + 2)

Multiply out the right side:

13T = 11T + 22

Subtract 11T from both sides:

2T = 22

Divide both sides by 2:

T = 11

Since the downstream trip takes 11 hours at 13 mph, the distance is 11 * 13 or 143 miles.


Check:

D = 11(T + 2)

143 ?= 11(11 + 2)

143 ?= 11 * 13

143 = 143 (answer is correct)

barge speed=12mph
water speed 1mph

upstream speed= barge speed-water speed=11mph=distanceAB/(t+2)
downstream speed= barge speed+water speed=13mph=distanceAB/t

distance AB from first relation is :11(t+2)
distance AB from the second relation is 13t

11(t+2)=13t
11t+22=13t
t=11
distance AB=11mph*13h=143miles

if distance is 99 as you say than there will be an error
upstream speed 11=99/(t+2) t=7
downstream 13=99/7 ;91does NOT equals 99

d/13=time going down stream
d/11=time going up stream=time going down stream + 2 hours
d/11=(d/13)+2
d=143 miles
99 is incorrect.