A3b to 30 km. if a , he is of b by 3/2 .of .

Initial speed:

Step-by-step explanation:

Both equations are concerned about the time differences between A and B. To avoid unknowns in the denominators,

First equation:

"A takes 3 hours more than B to walk 30 km."

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.

When A doubles his pace, he takes only 1/2 the initial time to cover the same distance. In other words, now it takes only hours for A to walk 30 km.

Second equation:

"[A] is ahead of B by 3/2 hours [on their 30-km walk.]"

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.

Hence the two-by-two linear system:

.

Solve this system for and :

Subtract the second equation from the first:

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.

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It initially takes 9 hours for A to walk 30 kilometers. The initial speed of A will thus be:

.

It takes 6 hours for B to walk 30 kilometers. The speed of B will thus be:

.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places