Question 939380
This is from that episode of Duck Dynasty, so I was just curious. Anyway, here it is:

Two trucks are traveling 1/4 mile to a store. Truck A is traveling 30 mph, and Truck B is traveling 15 mph. Truck B gets a 20 second head start. Which truck will get to the store first?
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Let time it takes slower truck, or Truck B to get to catch-up point, be T 
Then time it takes faster truck, or Truck A to catch-up to truck B is: {{{T - 20/3600}}}, or {{{T - 1/180}}} 

Since both had traveled same distance when truck A caught up to Truck B, we then get:
{{{15T = 30(T - 1/180)}}} 
{{{15(T) = 15(2)(T - 1/180)}}}
{{{T = 2(T - 1/180)}}}
{{{T = 2T - 1/90}}}
{{{T - 2T = - 1/90}}}
{{{- T = (- 1)/90}}} 
- 90T = - 1 ------- Cross-multiplying 
T = {{{(- 1)/(- 90)}}}, or {{{1/90}}} hour
Time taken by Truck B to get to catch-up point = {{{(1/90) * 3600}}}, or 40 seconds
Also, time taken by Truck A to get to catch up-point = {{{1/90 - 1/180}}}, or {{{2/180 - 1/180}}}, or {{{1/180}}}, or {{{(1/180) * 3600}}}, or 20 seconds 

The faster truck, or Truck A takes 20 seconds to catch up to Truck B at the {{{30(1/180)}}}, or {{{1/6-mile}}}, or 880-foot mark 
Now, since the distance to the store is: {{{1/4}}}-mile, or 1,320 ft, and Truck A caught up to Truck B at the
{{{1/6}}}-mile, or 880-ft mark, it’s obvious that Truck A clearly overtakes Truck B and reaches the store first