Question

Ernesto, the magnificent unicorn stallion, covered a distance of 50 kilometres on his first trip to Zalsazaria. On a later trip, he travelled 300 kilometres while going three times as fast. What was his new time compared with the old time?

Answer 1

Answer: The new time was twice as long as the old time.

Step-by-step explanation:

By definition:

$t=\frac{d}{V}$

Where "t" is time, "V" is speed and "d" is distance.

We know that Ernesto covered a distance of 50 kilometers on his first trip to Zalsazaria. This is:

$t_1=\frac{50}{V}$

On the later trip, he travelled 300 kilometers and he was going three times as fast ($3V$), then:

$t_2=\frac{300}{3V}$

Knowing this, we can compare those times:

$\frac{t_1}{t_2}=\frac{\frac{50}{V}}{\frac{300}{3V}}\\\\\frac{t_1}{t_2}=\frac{150V}{300V}\\\\\frac{t_1}{t_2}=\frac{1}{2}$

Solving for $t_2$ we get:

$t_1=\frac{1}{2}*t_2\\\\t_2=2t_1$

Answer 2

The new time when Ernesto is going 3 times as fast is about twice the old time

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let a represent the initial speed, hence:

a = 50/t

t = 50/a

For 300 km:

3a = 300/t'

t' = 100 / a = 2(50/a) = 2t

The new time when Ernesto is going 3 times as fast is about twice the old time

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