Question

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

Answer 1

Answer:

  his new time was twice as long

Step-by-step explanation:

At three times the original speed, Ernesto could cover 150 km in the same time as his original trip. The later trip is twice as far as that, so the second time is double the first time.

_____

At the same speed, time is proportional to distance.

Answer 2

Answer:

His new time is twice his old time :

$t_{2}=2t_{1}$

Step-by-step explanation:

• We need to use an equation that relates speed, distance and time. We are going to use the following equation :

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

Where ''v'' is the speed

Where ''d'' is the distance

And where ''t'' is the time

• We know by reading the exercise that :

$v_{1}=\frac{50km}{t_{1}}$ (I)

Where ''$v_{1}$'' is the speed of the first trip and where ''$t_{1}$'' is the time of the first trip.

• The equation of the second trip is :

$3v_{1}=\frac{300km}{t_{2}}$ (II)

Where ''$t_{2}$'' is the time of the second trip.

• If we use (I) in the equation (II) :

$3(\frac{50km}{t_{1}})=\frac{300km}{t_{2}}$ ⇒

$\frac{150km}{t_{1}}=\frac{300km}{t_{2}}$

$\frac{t_{2}}{t_{1}}=\frac{300km}{150km}$

$\frac{t_{2}}{t_{1}}=2$

$t_{2}=2t_{1}$

We find that the time of his second trip is twice as the first one.