Josh has been running for 6 min and completes a lap in 7 min. Gabe has been running for 2 min and completes a lap in 9 min.

How many more laps must Josh and Gabe complete to have run the same amount of time?

So j completed 6/7 of a lap

gabe has completed 2/9 lap

so

1 j lap=7 mins s o

7j

j=num of laps

1 g lap=9 mins so

9g

g=num of laps

then 6+j

and g+2

so

when will the times be equal

7j+6=9g+2

subtract 2 from both sides

7j+4=9g

divide both sides by 9

7/9j+4/9=g

so to get a whole number of laps, we must subsitute a number when it is multiplied by 7 then add 4, we get a multiplue of 9

so if j=2

7/9 (2) + 4/9=g=14/9+4/9=g=18/9=g=2

so josh and gabe must run 2 lap each because

6 + (2 times 7) = 2 + (9 times 2)

6+14=2+18

20=20

true so

the answer is 2 laps

Josh's speed is 1 lap/7 min

Gabe's speed is 1 lap/9 min

Josh has covered 6/7 of a lap

Gabe has covered 2/9 of a lap