I am in math 171 Pre-calculus algebra. I have no idea how to even start to answer this question. Any help would be much appreciated!! :) Thank you very much!

Question

A car traveling at 75 mph is passed by a second car going in the same direction at a constant speed. After 30 seconds, the two cars are (1/4) mile apart. Find the speed of the second car.

Answer 1

Let x = speed (in miles per hour) of second car

 

30 seconds = 1/120 hour

 

Distance = (Rate)(Time)

 

Distance traveled by first car 30 seconds after being passed

         

       = 75(1/120) = 15/24 = 5/8 mile

 

Distance traveled by 2nd car 30 seconds after passing the 1st car

 

       = x(1/120) = x/120

 

Distance of 2nd car - Distance of first car = 1/4

 

So, x/120 - 5/8 = 1/4

 

Multiply by 120:  x - 75 = 30

 

                              x = 105 mph 

Answer 2

Hi Mikey,

 

Sounds like an imposing problem for sure !!

 

We'll take it step by step - the old "divide and conquer" method.

 

Let's begin by writing an equation in words to express what's happening here:

    Fast Car Miles - Slow Car Miles = Miles Apart

 

The right side is easy - we are given it's 1/4 mile.

 

Let's come up with an expression for the miles traveled by the Fast Car:

    Distance = Rate x Time

    Rate = x mph (our unknown)

    Time = (30 sec)(1 min / 60 sec)(1 hr /60 min)

    Time = 30/3600 = 1/120 hr.

    Distance = (x)(1/120) = x/120 (Fast Car Miles)

 

Now let's follow the same procedure to come up with an expression for the miles traveled by the Slow Car:

    Distance = Rate x Time
    Rate = 75 mph (given)
    Time = (30 sec)(1 min / 60 sec)(1 hr /60 min)
    Time = 30/3600 = 1/120 hr.
    Distance = (75)(1/120) =

                        75/120 (Slow Car Miles)

 

Now let's plug these distance expressions for both cars back into our original word equation and solve for our unknown (x):

   Fast Car Miles - Slow Car Miles = Miles Apart

   x/120 - 75/120 = 1/4

   120(x/120) - 120(75/120) = 120(1/4)

   x - 75 = 30

   x = 30 + 75

   x = 105 mph (Fast Car Speed)

 

The trick to solving these complicated word problems is to first express in words an equation to represent what's stated.  Then we just come up with mathematical expressions to plug into our word equation, which will allows us to solve for our unknown.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.