Word problems of inequalities 2

Question

Tom’s home is 1800 m from his school. One morning he walked part of the way to school and then ran the rest. If it took him 20 minutes or less to get to school, and he walks 70 m/min and runs 210 m/min, how far did he run?

Answer 1

Let w = # of minutes Tom walked

Let r = # of minutes Tom ran

70w + 210r = 1800

w+r <= 20

7w + 21 r = 180

w+3r = 180/7

w+r = 20

2r = 180/7 - 20

r = 90/7 - 10

r = 20/7 Mins ~ 2.86 Mins

Tom ran at most for 2.86 Mins.