SOLUTION: 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 t

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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?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Two parallel time-lines helped in understanding the timing situation.

A___________0 mph for 0.00556 hour__________30 mph for x hour

B__________15 mph for x+0.00556 hour



A_________________

B_______________

Another arrangement is time for B is another variable, y.
Time quantity of y can be found.
, hour



Better understanding happens HERE:

Truck B having 20 seconds headstart, traveled 15*(0.00556) miles, BEFORE truck A began.
Truck B reached position 0.08333333 miles from starting point.

Now consider new time arrangement.
At time 0, A is at position 0, and B is at position 0.0833333.


----

Data table and using distances according to the positions from departure to 0.25 trip distance.

_____________________speed___________time_____________distance
A_____________________30_____________(1/4)/30_________1/4
B_____________________15_____________()_______________

Cleaning that a little bit,
_____________________speed___________time_____________distance
A_____________________30________________________1/4
B_____________________15_____________()____________

Solve for travel time of truck B, and then compare to the travel time of truck A.

The least time quantity corresponds to the truck which arrived first.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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?


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: , or  



Since both had traveled same distance when truck A caught up to Truck B, we then get:

 









 

- 90T = - 1 ------- Cross-multiplying 

T = , or  hour

Time taken by Truck B to get to catch-up point = , or 40 seconds

Also, time taken by Truck A to get to catch up-point = , or , or , or , or 20 seconds 



The faster truck, or Truck A takes 20 seconds to catch up to Truck B at the , or , or 880-foot mark 

Now, since the distance to the store is: -mile, or 1,320 ft, and Truck A caught up to Truck B at the

-mile, or 880-ft mark, it’s obvious that Truck A clearly overtakes Truck B and reaches the store first 

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