Question

Michael, Nate, Ben, and Andrew are running a relay race. In order to complete the race, they must run exactly 4 laps. Since Michael is the fastest of the four, he runs 1 1/3 laps. Nate then runs 1/2 lap, followed by Ben running 3/4 lap. How many laps must Andrew run to complete the race? Express your answer as a mixed number.

Answer 1

Andrew must run 1 5/12 Laps to complete the race.

Explanation:

Total lap run by Michael, Nate, Ben, and Andrew = 4 laps

laps run by Michael = 1 1/3 laps =(3+1)/3 = 4/3 laps

laps run by Nate =1/2 laps

laps run by ben =3/4 laps

Let laps run by Andrew = x

therefore

laps run by Michael + laps run by Nate + laps run by ben + laps run by Andrew = 4 laps

4/3 + 1/2 + 3/4 + x = 4

LCM of 3,2 and 4 is 12

=> (4*4 + 6*1 + 3*3+12x)/12 = 4

=> (16+6+9+12x)/12 = 4

=> 31+12x = 12*4 = 48

=> 12x = 48-31= 17

=> x = 17/12 = 1 5/12

Thus, Andrew must run 1 5/12 Laps to complete the race.