Question

Two comets orbit the sun. One comet travels $30,000$ miles per hour and the other comet travels $28,500$ miles per hour. What is the most efficient way to calculate the difference in the distances traveled by the comets for any given number of minutes? Justify your answer.

Answer 1

The most efficient way to calculate the difference in the distances traveled by the comets for any given number of minutes is by using the distance-traveled formula. Which says $\mathrm{Distance}\mathrm{traveled}=\mathrm{speed}\times \mathrm{time}$.

Justification:

Step 1: Change the speed of the comet in $miles/minute$

Speed of Comet $1$ : $30,000$ miles per hour

$=30,000\times \frac{1}{60}=500miles/minute$ [Considering $60minutes$ in an hour.]

Speed of Comet $2$ : $28,500$ miles per hour

$=28,500\times \frac{1}{60}=475miles/minute$ [Considering $60minutes$ in an hour.]

Step 2: Find the difference in distance traveled.

Let us assume that the time of travel is $tminutes$

Then by using formula $\mathrm{Distance}\mathrm{traveled}=\mathrm{speed}\times \mathrm{time}$,

Distance traveled by Comet $1$$=500\times t=500tmiles$

Distance traveled by Comet $2$$=475\times t=475tmiles$

Difference$=500t-475t=25tmiles$

Therefore, the difference in the distance traveled is $25tmiles$.