Question

PLZ HELP OR I FAIL MY TEST

Answer 1

Answer:

time upstream=24/8=3 hours

time downstream=24/12=2 hours

Step-by-step explanation:

If R*T=D, and R is speed + or - current, how can you find the rate without the time, and how can you find the time without the rate?

THE KEY WAS WHEN WE WERE TOLD THAT IT TAKES ONE HOUR LONGER TO GO UPSTREAM THAN DOWNSTREAM BECAUSE T=D/R AND WE ARE TOLD THAT:

D/R(Upstream) minus 1 equals D/R (DOWNSTREAM)

Let x=rate of current

distance(d)=rate(r) times time(t) or d=rt or t=d/r

distance upstream=distance downstream=24 mi

rate upstream=10-x

rate downstream=10+x

time upstream=(distance upstream)/(rate upstream)=24/(10-x)

time downstream=(distance downstream)/(rate downstream)=24/(10+x)

Now, we are told that time upstream minus one hour equals time downstream. So our equation to solve is:

24/(10-x)-1=24/(10+x) Multiply both sides by (10-x)(10+x)

24(10+x)(10-x)/(10-x)-1(10-x)(10+x)=24(10-x)/(10+x)/(10+x) clear fractions

24(10+x)-(10-x)(10+x)=24(10-x) clear parens

240+24x-100-10x+10x+x^2=240-24x subtract 240 from and add 24x to both sides

240-240+24x+24x-100+x^2=240-240-24x+24x collect like terms

x^2+48x-100=0 ----------------quadratic equation in standard form

This equation can be factored:

(x+50)(x-2)=0

x=-50 mph----------------discount the negative value for speed

and

x=2 mph----------------------speed of the current

CK

10-x=10-2= 8 mph -----------------------speed upstream

10+x=10+2=12 mph--------------------------speed downstream

time upstream=24/8=3 hours

time downstream=24/12=2 hours

so 3-2=1----takes 1 hour longer upstream