HELP ME PLEASE

Question

Jared is training for a cross-county cycling race. He rode 42 miles in 2 hours. After the first 32 miles through the foothills, he increased his speed by 5 miles per hour as he rode on flat roads for the last 10 miles. Find Jareds cycling speed through the foothills

Answer 1

distance=rate*time

d=rt

32=rt -------------> 32/r=t

10=(r+5)(2-t)

substitute

10=(r+5)(2-[32/r])

10=2r+5*2-[32/r]r-5[32/r]

10=2r+10-32-160/r

10=2r-22-160/r

10r=2r^2-22r-160

2r^2-22r-10r-160=0

2r^2-32r-160=0

r^2-16r-80=0

factor

(r-20)(r+4)=0

r-20=0

r=20 mph in the foothills  (answer)