Distance Word Problems

Question

Lito can get to his office,which is 14 mi away, by riding a bus for 30 min and walking for 30 min. When he wants more exercise, he gets there by riding the bus for 25 min and walking for 1 h. What are his average walking rate and the average speed of the bus?

Answer 1

14=(1/2)r+(1/2)w  where r=rate of the bus and w= walking rate

14=(5/12)r+(1)w

multiply first equation by 2

28=r+w

from second equation 14=(5/12)r+w get 14-(5/12)r=w

substitute

28=r+14-(5/12)r

28=14+(7/12)r

28-14=(7/12)r

14=(7/12)r

multiply by (12/7)

(12/7)(14)=(12/7)(7/12)r

24=r, r=24 mph for the bus

14=(1/2)(24)+(1/2)w

14=12+(1/2)w

14-12=(1/2)w

2=(1/2)w

w=4 mph for the walking rate