pablo can drive 3 times as fast as pedro can ride his bike if it takes pedro 2 hrs longer than pablo to travel 84 miles how fast can pedro ride his bike

Question

pablo can drive 3 times as fast as pedro can ride his bike if it takes pedro 2 hrs longer than pablo to travel 84 miles how fast can pedro ride his bike

Answer 1

Hi Amber,

 

Let's begin by writing algebraic expressions to represent the two rates:

    x = Pedro's rate (mph)

    3x = Pablo's rate (mph)

 

Next, let's write an equation to express the relationship between the two times using the given distance and our algebraic expressions for the two rates:

    distance = rate x time

    time = distance / rate

    Pablo's time:  84/3x

    Pedro's time:  84/x

    84/3x + 2 = 84/x (two hours longer for Pedro)

 

Next, let's solve our equation for x (Pedro's rate):

    84/3x + 2 = 84/x

    (3x)(84/3x) + (3x)(2) = (3x)(84/x)

    84 + 6x = 252

    6x = 252 - 84

    6x = 168

    x = 28 mph (Pedro's rate)

 

We can verify our answer by plugging it back into our equation and checking to see that both sides are equal:

    84/3x + 2 = 84/x

    84/[(3)(28)] + 2 = 84/28

    84/84 + 2 = 3

    1 + 2 = 3

    3 = 3 (both sides are equal)

 

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

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan (Romans 5:8).