Robert was going to school at a speed of 4 mph. After completing half the distance, he realized that he had forgotten his assignment at home. So, he ran toward home and then back to school at a speed of 12 mph.

Find the total time Robert took to cover the entire distance, if the total distance between his home and school is 6 miles.

Total distance between Robert's home and school = 6 miles
$Halfofthetotaldistance=\frac{6}{2}=3miles$

We know,
$Speed=\frac{Distance}{Time}$

So,
$Time=\frac{Distance}{Speed}$

• Robert covered half the distance at a speed of 4 mph.

$Timetaken=\frac{3}{4}h$

• After realizing that he had left his assignment, he ran the half distance to his home at the speed of 12 mph.

$Timetaken=\frac{3}{12}=\frac{1}{4}h$

• He ran from his home to school and covered the total distance at a speed of 12 mph.

$Timetaken=\frac{6}{12}=\frac{1}{2}h$


Total time taken by Robert to reach school,
$=\frac{3}{4}+\frac{1}{4}+\frac{1}{2}$

$=\frac{3+1+2}{4}$ (LCM of denominators = 4)

$=\frac{6}{4}h$

$=\frac{3}{2}h$

$=1.5h$

Thus, Robert took 1.5 hours to reach his school.