Question

Please help me answer this

Answer 1

`D)\ 25\%`

Explanation:

The following equation can be used to relate the speed time and distance of an object in motion,

`(Speed)*(Time)=(Distance)`

One can also rewrite this equation in terms of time:

`(Speed)=((Distance))/((Time))`

Let this equation represent the relation between Mr.Wang's initial speed and travel time. However, in this problem, Mr.Wang faced a decrease in his speed, more specifically, a (20%) decrease. Subtract (0.2) from (1) to find Mr.Wang's speed in relation to his original speed. Let (x) represent the increase in time that Mr. Wang had to incur in order to reach his destination. Model this situation,

`(Speed)*(Time)=(Distance)`

`0.8(Speed)*x(Time)=(Distance)`

Now use inverse operations to solve for the coefficient (x):

`0.8(Speed)*x(Time)=(Distance)`

`x(Time)=((Distance))/(0.8(Speed))`

Using the relation state above: (
`(Speed)=((Distance))/((Time))`) one can state the following:

`x(Time)=((Distance))/(0.8(Speed))`

`x(Time)=(1)/(0.8)(Time)`

Thus, (Time) can be omitted from this equation, as it appear on both sides as a factor, hence one can then solve for (x):

`x(Time)=(1)/(0.8)(Time)`

`x=(1)/(0.8)`

Divide (1) by (0.8):

`x=(1)/(0.8)\\x=0.25`

Multiply the decimal by (100) to put it into the percent form:

`x=0.25\\x=25\%`