SOLUTION: a boat goes upstream 30 miles and downstream 44 miles in 10 hours.the next day it goes upstream 40 miles and downstream 55 miles in 13 hours.what is the average speed of the boat a

Question 125513: a boat goes upstream 30 miles and downstream 44 miles in 10 hours.the next day it goes upstream 40 miles and downstream 55 miles in 13 hours.what is the average speed of the boat and the stream?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a boat goes upstream 30 miles and downstream 44 miles in 10 hours.the next day it goes upstream 40 miles and downstream 55 miles in 13 hours.what is the average speed of the boat and the stream?
:
Let x = speed of the boat in still water
Let y = speed of the current:
then
(x-y) = speed upstream
(x+y) = speed downstream
:
Write a time equation for the 1st trip: time =
:
Time upstream + time down stream = 10 hrs
+ = 10
:
Do the same for the second trip:
+ = 13
:
We can use elimination; multiply the 1st eq by 4, and the 2nd eq by 3:
+ = 40
+ = 39
---------------------------subtraction eliminates leaving us with
= 1
which is:
x + y = 11
:
We can replace(x+y) with 11 in the 1st trip equation
+ = 10
+ 4 = 10
= 10 - 4
= 6
Cross multiply
6(x-y) = 30
x - y = 5; divided equation by 6
:
Using these two simple equation eliminate y
x + y = 11
x - y = 5
-------------adding eliminates y
2x = 16
x = 8 mph is the boat in still water
then
8 + y = 11
y = 3 mph is the current
:
:
Check our solution in the 2nd trip equation:
+ = 13
:
:
Seems like there should be a simpler way, but I can't seem to come up with tonight.

RELATED QUESTIONS
A Boat goes upstream 40 miles and downstream 86 miles in 8 Hours. If it goes upstream 24... (answered by ankor@dixie-net.com)

Please help a boat goes 24 miles upstream in 2 hours. it goes 36 miles downstream also (answered by Alan3354)

sammy owns a motor boat that travels 4 miles/hour in still water. It goes 12 miles... (answered by mananth)

A boat goes up stream 30 miles and down stream 44 miles in 10 hours. Again it goes up... (answered by ptaylor)

A boat goes 24 miles upstream in 2 hours. It goes 36 miles downstream also in 2 hours.... (answered by mananth)

If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate... (answered by stanbon)

If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate... (answered by ankor@dixie-net.com)

If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate... (answered by checkley75)

If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the... (answered by checkley71)