i drove from home to work at 30 mph. after work traffic was heavier and drove home at 25 mph. my driving time to and from work was 1 hour and 6 minutes. how far

Question

do i live from work?

Answer 1

distance=rate*time

d=rt

d=30*t

d=25*(11/10-t) because 6 minutes=6/60=1/10 of an hour

equate the two right sides

30t=25(11/10-t)

30t=275/10-25t)

30t+25t=27.5

55t=27.5

t=27.5/55

t=1/2 hour

d=30*(1/2)=15 miles from home

Answer 2

First thing we need to recall is the distance formula:  d=rt

 

For the trip from home to work d = 30t₁

For the trip home from work d = 25t₂ 

 

We know that t₁ + t₂ = 1 hour 6 minutes or 1.1 hours

Since d = 30 t₁, then t₁ = d/30

And since d=25 t₂, then t₂ = d/25

 

We can substitute these two, above.

 

d/30 + d/25 = 1.1

5d/150 + 6d/150 = 1.1

 

Combining terms

11d/150 = 1.1

 

Multiply both sides by 150

11d = 165

 

Divide both sides by 11

d = 15 miles

 

We can check this as follows

 

To work from home we travel 15 miles at 30 mph.  This takes 0.5 hour (15/30).

Back home from work we travel 15 miles at 25 mph.  This takes 0.6 hour (15/25)

 

0.5 + 0.6 = 1.1 hours

 

 

 

Answer 3

This is a problem that uses the formula D=RT (distance equals rate times time).

 

Since the distance is the same in both directions and we know the total time we can determine the time in each direction by thinking of the above formula as T=D/R, and then add those times together to get total time.

 

So the time from home to work is represented by D/30. The trip home took D/25 (heavier traffic). Since the rates are given in miles per hour the 1 hour and 6 minutes must be represented in hours. That is 1 and 6/60 of an hour or 1 1/10 or 11/10 of an hour.

 

Now we add the two times and set equal to 11/10.

 

D/25 + D/30 = 11/10

 

There are a few different ways to solve for D at this point. My preference is to multiply both sides of the equation by the LCD of 25, 30, 10. That happens to be 300.

 

Multiplying every term by 300 results in:

 

12D + 10D = 330

 

22D = 330

 

D = 330/22 = 15 (miles).