Word problems

Question

Bill left his house at 2 pm and rode his bike down Main Street at a speed of 12 mi/h. When his friend Mary arrived at his house at 2:10 pm, Bills mother told her the direction in which Bill went, and Mary cycled after him at a speed of 16 mi/h. At what time did Mary catch up with Bill?

Answer 1

Let T be the total time Bill is riding his bike

 

so,

 

the total time Mary is riding her bike (T - 1/6) since Mary left the house 10 minutes after Bill

 

12T = 16(T - 1/6)

 

12T = 16T - 16/6

 

16/6 = 16T - 12T

 

16/6 = 4T

 

T = 2/3 hours

 

so, the time is 2:40 pm.