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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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_________________0%2A%280.00556%29%2B30x

B_______________15%28x%2B0.00556%29

Another arrangement is time for B is another variable, y.
Time quantity of y can be found.
%281%2F4%29%2F15=1%2F60, 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_____________(t)_______________0.25-0.08333

Cleaning that a little bit,
_____________________speed___________time_____________distance
A_____________________30_____________1%2F120___________1/4
B_____________________15_____________(t)____________0.25-0.08333

Solve for travel time of truck B, and then compare to the travel time of truck A. t=%280.25-0.08333%29%2F15

The least time quantity corresponds to the truck which arrived first.

Answer by MathTherapy(10552) About Me  (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: T+-+20%2F3600, or T+-+1%2F180 



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

15T+=+30%28T+-+1%2F180%29 

15%28T%29+=+15%282%29%28T+-+1%2F180%29

T+=+2%28T+-+1%2F180%29

T+=+2T+-+1%2F90

T+-+2T+=+-+1%2F90

-+T+=+%28-+1%29%2F90 

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

T = %28-+1%29%2F%28-+90%29, or 1%2F90 hour

Time taken by Truck B to get to catch-up point = %281%2F90%29+%2A+3600, or 40 seconds

Also, time taken by Truck A to get to catch up-point = 1%2F90+-+1%2F180, or 2%2F180+-+1%2F180, or 1%2F180, or %281%2F180%29+%2A+3600, or 20 seconds 



The faster truck, or Truck A takes 20 seconds to catch up to Truck B at the 30%281%2F180%29, or 1%2F6-mile, or 880-foot mark 

Now, since the distance to the store is: 1%2F4-mile, or 1,320 ft, and Truck A caught up to Truck B at the

1%2F6-mile, or 880-ft mark, it’s obvious that Truck A clearly overtakes Truck B and reaches the store first