Question

A rabbit lure on a greyhound racetrack is set to travel once around the track at 50 feet per second, and then its speed is increased to 65 feet per second for the second loop around the track. If the total time it takes for the lure to go around the track twice is 184 seconds, what is the distance once around the track?

can I get a detailed answer on how to solve this and what formula a would need to use?

Answer 1

its the same concept of different speeds being used.
understand this: time taken=distance/speed
we hav been given total time taken.this has to be equal to the sum of individual lap timings.... therefore solve x/50+x/65=184 for x . and answer is n feet.

Answer 2

how would I start to solve that?

Answer 3

take lcm and proceed.

Answer 4

sorry i dont understand

Answer 5

ok it like this,

x/50+x/65=1/5(x/10+x/13)=23x/(5*130)=184(taking least common multiple(lcm))
=> x=184*5*130/23
get it?

Answer 6

so it would be 5200...?

Answer 7

yea it comes out to be 5200 .

Answer 8

A rabbit lure on a greyhound racetrack is set to travel once around the track at 40 feet per second, and then its speed is increased to 50 feet per second for the second loop around the track. If the total time it takes for the lure to go around the track twice is 135 seconds, what is the distance once around the track?

ok so for this one I have x/40+x/50=135 so far whats my next step?

Answer 9

u essenstially need an expression which looks like kx=135...so for finding k we need to add (1/40+1/50) ... this can be done by considering lcm, which is (1/10(1/4+1/5))=9/200
therefore, its is now 9x/200=135 . understood the method?