a motor boat move 18 mph in still water. it travels 35 miles upstream and 35 miles downstream in total time of 4.0 hours. what is the speed of the current?

Question

anonymous · Answer

this is a bit long but it is step by step
time = distance/speed over the ground

time upstream = distance/ (boatspeed - current)
time downstream = distance/(boatspeed + current)

time overall = distance/(boatspeed - current) + distance/(boatspeed + current)

Now we need to trun this around to find the current
Start by substitute in the numbers we know and replace current with x

4 = 35/(18-x) + 35/(18+x)

Now get rid of the fractions

multiply both sides by (18-x)
4 (18 -x) = 35 + 35(18-x)/(18+x)

multiply both sides by (18+x)
4 (18 -x)(18+x) = 35(18+x) + 35(18-x)

multiply out
4 (324 - 18 x + 18x -x^2) = 630 + 35x + 630 - 35x

The x's cancel out leaving
4 (324 - x^2) = 1260

multiply out again
1296 - 4 x^2 = 1260

-1260 from both sides
1296 - 1260 -4x^2 = 0

36 - 4x^2 = 0

add 4 x^2 to both sides
36 = 4x^2

9 = x^2

so 
x=3