Question

Greg drove to school at 30 mph to drop off his friend’s car. He then jogged home at 6 mph. If the entire trip too k him 1 hour, how far does he live from school?

Answer 1

Answer: He lives 5 miles from school.

Solution:

Let distance between school and home be x miles.

Grey drove to school at speed = 30 mph

Distance between school and home = x mile

Formula used: $Time=\frac{Distance}{Speed}$

Time taken by Grey from home to school  $T_1=\frac{x}{30}$

Grey jogged to home at speed = 6 mph

Distance between school and home = x mile

Formula used: $Time=\frac{Distance}{Speed}$

Time taken by Grey from home to school  $T_2=\frac{x}{6}$

Grey took 1 hour for entire trip.

Therefore, $T_1+T_2=1$

$\frac{x}{30}+ \frac{x}{6}=1$

$\frac{x}{30}+ \frac{5x}{30}=1$

$\frac{6x}{30}=1$

we get , x=5 miles.

He lives 5 miles from school.

Answer 2

5 miles

using the formula

time = $\frac{distance(d)}{speed}$, then his distance can be calculated

$\frac{d}{30}$ + $\frac{d}{6}$ = 1

$\frac{d}{30}$ + $\frac{5d}{30}$ = 1

$\frac{6d}{30}$ = 1 ( multiply both sides by 30 )

6d = 30 ( divide both sides by 6 )

d = 5

He lives 5 miles from school