Please solve

Question

Please solve in algebra format

 

Gene spent 10 min riding his bicycle to a friend’s house. He left his bike there and with his friend, walked for 15 mins to the gym. Gene rides his bicycle 10km/h faster than he walks. If the entire trip covered a distance of 2.75km, how far is it from the friend’s house to the gym?

Answer 1

distance=rate*time

d=rt

r+10=rate riding his bike

r=rate walking

10 minutes=10/60 hours

15 minutes=15/60 hours

distance=rate*time(riding)+rate*time(walking)

2.75=(r+10)(10/60)+(r)(15/60)

2.75=(r+10)(1/6)+(r)(1/4)

multiply both sides by 12

33=(r+10)2+(r)3

33=2r+20+3r

33=5r+20

13=5r

r=13/5=2.6 km per hour (walking)

d=rt

d=2.6*(15/60)

d=2.6*(1/4)

d=0.65 km to the gym from the friend's house

d=12.6(10/60)

d=12.6(1/6)

d=2.1 km to the friend's house

2.1+0.65=2.75 km total distance as stated in the problem