Tom leaves town at 8:00 AM and drives north at an average speed of 50 mph. Bill leaves town at 10:30 AM and drives north on the same highway at 65 mph...

Question

Tom leaves town at 8:00 AM and drives north at an average speed of 50 mph. Bill leaves town at 10:30 AM and drives north on the same highway at 65 mph. at what time will bill catch up to tom?

 

PLEASE HELP AND SHOW ALL WORK

Answer 1

Danny,

This one is a little more straight forward. Again we use d = vt

But this time they are inherently separate equations, and we want to know when they are equal.

 

d_t = v_tt_t

d_b = v_bt_b

 

When does d_t = d_b ?

 

v_tt_t = v_bt_b

 

50t_t = 65t_b Now we need a relationship between t_t and t_b to remove one variable.

 

Since Bill left 2.5 hours later, we'll say t_t = t_b + 2.5

 

Now substitute into the first equation

 

50(t_b + 2.5) = 65t_b

 

50t_b + 125 = 65t_b

 

125 = 15t_b

 

25/3 = t_b

 

8 hr 20 min = t_b

 

But they didn't ask how long, they asked what time. Therefore:

 

10:30 AM + 8hr 20min = 6:50 PM