Question

After sailing 15 miles, a sailor changed direction and increased the boat's speed by 2mph. An additional 19 miles was sailed at the increased speed. The total sailing time was 4 hours. FIND THE RATE OF THE BOAT FOR THE FIRST 15 MILES.
Is this formula correct that I set up?
15/r=19/2r+2=4 hours
I know that the time being the same I can set them equal to one another

Answer 1

sorry didn't mean to repeat the question

Answer 2

I have my formula corrected in this second one

Answer 3

ok so you have the correct equation you just need to solve for r
combine fractions on left side
cross multiply
add like terms
i think you will get a quadtratic so use quadratic formula

Answer 4

Ok I got 15(2r)=19r+4r^2=8r^2?? Is that right?

Answer 5

hmm not quite
it should be r+2 not 2r
15/r + 19/r+2 = 4

Answer 6

sorry I thought because he increased by 2 miles per hour that it was going to be times
how can I tell the difference?

Answer 7

if i said i doubled my speed then i went from 10mph to 20mph
i multiplied by 2
if i said i increased my speed by 4mph, then i went from 10mph to 14 mph
i added 4

Answer 8

ohhh

Answer 9

thanks dumbcow

Answer 10

your welcome
after you combine fractions you should get
15(x+2) + 19x = 4x(x+2)
oh i used x instead of r

Answer 11

Yes, thank you for making sure I got the quadractic right. I stumble sometimes when I am combining

Answer 12

d = rt

15 = xt let x be the first rate
19 = (x + 2)t

solve both for t

15
-- = t
x

19
----- = t
x + 2

We know their combined time was 4 hours.. so we will add these together to get 4

15 19
-- + ----- = 4
x x+2

common denominator of x(x + 2) you multiply every term by that

x(x+2)15 x(x+2)19 x(x+2)4
-------- + -------- =
x x + 2

cancel the bottoms into the tops

(x + 2)15 + x(19) = 4x(x+2)

15x + 30 + 19x = 4x^2 + 8x

34x + 30 = 4x^2 + 8x

0 = 4x^2 - 26x - 30

0 = 2(2x^2 - 13x - 15)

0 = 2(2x - 15)(x + 1)

x = 15/2 or -1 since hours can't be negative we use the 15/2

15/2 = 7.5

x = 7.5 mph

Answer 13

thank you blextiing

Answer 14

I missed my quadractic like I knew I would putting a 32 where there was supposed be a 36
i mean 26