D=rt (how long did it take)?

Question

Tina hiked 15 km up a mountain, and hiking down took 30 min less as her speed went up by 1 km. How long did the climb take her.

Answer 1

d=rt

15=rt (up)

15=(r+1)(t-0.5) (down)

15=rt means 15/r=t

substitute

15=(r+1)(15/r-0.5)

multiply both sides by r

15r=(r+1)(r)(15/r-0.5)

15r=(r+1)(15-0.5r)

15r=15r+15-0.5r²-0.5r

15r=14.5r+15-0.5r²

0=-15r+14.5r+15-0.5r²

0=-0.5r+15-0.5r²

0=0.5r²+0.5r-15 (multiplied both sides by -1)

0=r²+r-30 (multiplied both sides by 2)

factor

(r+6)(r-5)=0

r-5=0

r=5 km/hr up the mountain

15=5t

15/5=t

t=3 hours to climb up the mountain