Mike drives to work and back home using the same route.
On his way, there is traffic and he averages a speed of 40 miles per hour (mph). On his way back, when there is no traffic, he averages 60 mph. If the total driving time going to and from work is 1 hour and 10 minutes,
how far, in miles, is his workplace from his home?
The general rate equation is given as the following:
d=rt
Where
d= distance
r= rate or speed
t= time
Since there is a different rate going to and from work, we need to take two cases:
To work
d=rt
d=40t1
t1=40d
From work
d=rt
d=60t2
t2=60d
We know that the time will add up to 1 hour and 10 minutes, which is the same as 161 hours.
t1+t2=161
40d+60d=161
1203d+1202d=67
1203d+2d=67
1205d=6⋅207⋅20
5d=140
d=28
We can test the answer choices. For example, here is how we would test the answer, 28.
To work
d=rt
28=40t
4028=t
107=t
From work
d=rt
28=60t
6028=t
157=t
Total time=107+157
67=107+157
67=3021+3014
67=3035
67=67 ✓