Question

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?

Answer 1

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

Answer 2

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