Combination of functions

Question

Two little dogs, 100 meters apart on the same path, are running towards one other. Dog A has a speed of 4 meters each second; Dog B has a speed of 6 meters each second. Let’s suppose they start to run to each other when t=0. How long will it take for the dogs to bump into one another?

Answer 1

Hi Allycia,

 

Let's begin by knowing that the dogs would have each been running for the SAME amount of time (t) when they bump into each other.  

 

Therefore, since we know the rate of each dog, we can write this equation to express the sum of their distances as being equal to the initial distance separating them:

    distance = rate x time

    100 = 4t + 6t  (equation)

 

Solving for time (t):

    10t = 100

    t = 100/10

    t = 10 seconds

 

We can verify our answer by plugging it back into the equation to see if both sides prove equal:

    100 = 4t + 6t 

    100 = 4(10) + 6(10)

    100 = 40 + 60

    100 = 100 (both sides proven equal)

 

Since both sides of the equation have been proven equal with our plugged-in answer, we are confident that our answer is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.