Question

Beatrice participates in professional triathlons. She runs 2 mph faster than her friend Joe, a weekend athlete. If they each

Answer 1

Speed of  Joe is 6  mph and that of  Beatrice  is 8 mph

Step-by-step explanation:

Let Joe's speed be S

Beatrice's speed be s + 2

Let  Joe's time be  T

Beatrice's time = T - 1/2

Then

We know that

$speed = \frac{distance}{time}$

Now

Distance  =$speed \times time$

On substituting the value

Equation corresponding to Joe

$12 = S \times T$...........................(1)

 Equation corresponding to Beatrice

$(S+2) \times (T - \frac{1}{2})=12$

Now solving for s and T,we get

$(S+2) \times (\frac{12}{S}- \frac{1}{2})=12$

$(S+2) \times (\frac{24 -S}{2S})=12$

$2S(S+2) \times ({24 -S})=12(2S)$

$(2S^2 - 4S )(24-S) = 24S$

S = 6 mph -------------------------- Joe's speed

T = 2 hours ------------------------ Joe's time

Thus Beatrice's speed  is

6 + 2 = 8 mph

Beatrice's time is

$2 -\frac{1}{2} =1\frac{1}{2 }hours$