what is the distance driven?

Question

Amy drove from Denver to boulder during rush hour at an average speed of 30mph and drove home at an average speed of 45mph.  If the round trip took 1.75 hours, how far is it from Boulder to Denver?

Answer 1

d=rt

d=30t

d=45(1.75-t)

30t=45(1.75-t)

30t=78.75-45t

75t=78.75

t=78.75/75=1.05 hours at 30 mph

1.75-1.05=0.7 hours at 45 mph

distance=30*1.05=31.5 miles or,

distance=45*0.7=31.5 miles

Answer 2

The time to drive from Denver to Boulder at 30 MPH takes D/30 hours, where D is the distance.

Similarly, the drive from Boulder to Denver at 45 MPH takes D/45 hours.

 

The round trip, therefore takes

D/30  +  D/45 hours.

 

The LCD is 90, so we will multiply the first fraction by 3/3 and the second by 2/2, giving

3D/90 + 2D/90 = 5D/90.

 

But this simplifies to D/18.

 

We know that the round trip took 1.75 hours. This gives the equation:

D/18 = 1.75 Multiply both sides by 18.

D = 18 * 1.75 = 31.5

 

Answer 3

if the first trip (30 mi/hr) took t1 hours and the second (45mi/hr) took t2 hours, and it's a round trip with the same distance between the two points, then we'll have:

 

30*t1=45*t2

 

we also know that the whole driving time was 1.75 hours, so we can say:

 

t1+t2=1.75

 

solving this system of two equations with two unknowns (t1,t2), we'll find:

 

t1=1.05hr, t2=0.7hr

 

then the distance between the two points would be:

 

distance=30*t1=45*t2=31.5 miles

Answer 4

“Amy drove from Denver to Boulder during rush hour at an average speed of 30mph and drove home at an average speed of 45mph. If the round trip took 1.75 hours, how far is it from Boulder to Denver?”

t0 = left Denver = 0

t1 = time arrived in Boulder

t2 = time left Boulder

t3 = time arrived home

d = distance driven from Boulder to Denver and back on some repeated route not necessarily the shortest nor the Google Maps route.

d = 30(t1 - t0) = 45(t3 - t2) => (t3 - t2) = 30/45 t1

1.75 = (t1 - t0) + (t3 - t2) = t1 + 30/45 t1

t1 = 1.75/(1+2/3) = 1.75*3/5 = 3*0.35 = 1.05 hours

d = 30 t1 = 31.5 miles