A cheetah that is running 90 feet per second is 120 feet behind an antelope that is running 60 feet per second. How long will it take cheetah to catch up to the antelope?

Question

Nicole Conner · Accepted Answer

Formula Used:  Distan⁡ce=speed×time  Let the time taken by cheetah to catch up to the antelope be t seconds.  The distance travelled by Cheetah in t seconds =90x  The distance travelled by Antelope in t seconds =60x  As, in t seconds Cheetah catches up to antelope, so,  90x−60x=120  30x=120  x=12030  x=4  Conclusion:  Thus, the time taken by cheetah to catch up to the antelope is 4 seconds.

Eliza Beth13 · Accepted Answer

Result:We used the equation dc=da+120 to represent the distances covered by the cheetah and the antelope. By solving this equation, we found that the cheetah would catch up to the antelope after 4 seconds.Solution:Let&#039;s assume that the cheetah catches up to the antelope after time t seconds. During this time, the cheetah will have covered a distance equal to its velocity multiplied by the time taken, and the antelope will have covered a distance equal to its velocity multiplied by the time taken.The distance covered by the cheetah can be expressed as dc=90t feet, and the distance covered by the antelope can be expressed as da=60t feet.Given that the cheetah is initially 120 feet behind the antelope, we can set up the equation:dc=da+120Substituting the expressions for dc and da:90t=60t+120Now, we can solve this equation for t:90t−60t=12030t=120t=12030t=4 secondsTherefore, it will take the cheetah 4 seconds to catch up to the antelope.

madeleinejames20 · Accepted Answer

Given:t=dvwhere:- t is the time taken,- d is the distance between the cheetah and the antelope, and- v is the relative velocity of the cheetah with respect to the antelope.Given that the cheetah is 120 feet behind the antelope, we have d=120 feet. The relative velocity of the cheetah with respect to the antelope is the difference between their speeds, so v=90−60=30 feet per second.Plugging these values into the equation, we get:t=12030=4 seconds.Therefore, it will take the cheetah 4 seconds to catch up to the antelope.

Nick Camelot · Accepted Answer

Step 1:The distance traveled by the cheetah in t seconds can be calculated by multiplying its speed (in feet per second) by the time:Distance&amp;nbsp;traveled&amp;nbsp;by&amp;nbsp;the&amp;nbsp;cheetah=Speed&amp;nbsp;of&amp;nbsp;the&amp;nbsp;cheetah×tSimilarly, the distance traveled by the antelope in t seconds is given by:Distance&amp;nbsp;traveled&amp;nbsp;by&amp;nbsp;the&amp;nbsp;antelope=Speed&amp;nbsp;of&amp;nbsp;the&amp;nbsp;antelope×tStep 2:Given that the cheetah is initially 120 feet behind the antelope, we can set up the following equation:Distance&amp;nbsp;traveled&amp;nbsp;by&amp;nbsp;the&amp;nbsp;cheetah=Distance&amp;nbsp;traveled&amp;nbsp;by&amp;nbsp;the&amp;nbsp;antelope+Initialdistancebetweenthem90t=60t+120Simplifying the equation, we get:30t=120Step 3:To solve for t, we divide both sides of the equation by 30:t=12030Simplifying further:t=4 secondsTherefore, it will take the cheetah 4 seconds to catch up to the antelope.

A cheetah that is running 90 feet per second is 120 feet behind an antelope that

Answered question

Answer & Explanation

New Questions in Algebra II