problem solving

Question

I don't know how to set up this problem.   

 

A family goes on vacation to a water park. During the drive to the water park the weather caused the family to average 44 miles per hours. After their vacation the weather improved, so they could average 77 miles per hour on the return trip. If the distance each way was equal, and the entire time driving was 11 hours, find the distance one way to the water park.

Answer 1

There are three unknowns in this problem- the distance, and the times of travel in each direction. However, since we know the total travel time is 11 hours, then if T  is the time in the forward direction, 11-T must be the time for the reverse trip.

 

Let D = distance to the water park.

Speed = distance/time

77 = D/T

44 = D/(11 - T)

 

Solve these two equations to determine D.

Answer 2

distance=rate*time

d=r*t

d=44*t  (to the park)

d=77*(11-t)

44t=77(11-t)

divide both sides by 11

4t=7(11-t)

4t=77-7t

4t+7t=77

11t=77

t=77/11

t=7 hours

d=44*7

d=308 miles, or...

d=77*4=308 miles again