SOLUTION: Suppose that a trip from the dormitory to the lake at 30 mi/h takes 12 min longer than the return trip at 48 mi/h. How far apart are the dormitory and the lake?

Question 221040: Suppose that a trip from the dormitory to the lake at 30 mi/h takes 12 min longer than the return trip at 48 mi/h. How far apart are the dormitory and the lake?
Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Suppose that a trip from the dormitory to the lake at 30 mi/h takes 12 min longer than the return trip at 48 mi/h. How far apart are the dormitory and the lake?

Step 1. distance = speed * time.

Step 2. distance = 30 *(x+12) where x is the time it takes for the return trip at 48 mi/hour or 48 mi/60 minutes

Step 3. distance = 48x for the return trip.

Step 4. Set the distance in Steps 2 and 3 to be equal. Then,

Subtract 30x to both sides of the equation

Divide 18 to both sides of the equation

Step 5. Then x=20 minutes traveling at 48 km/hr and distance is 20 minutes* 48 km/hr * 1 hr/60 minutes = 20*48/60= 20*4/5= 16 km.

Check....30*(20+12)/60=-30*32/60=16 km at 30 km/hr at 32 minutes (20+12 minutes).

Step 6. ANSWER: The distance between the lake and dormitory is 16 km.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
Suppose that a trip from the dormitory to the lake at 30 mi/h takes 12 min longer than the return trip at 48 mi/h. How far apart are the dormitory and the lake?

Let distance between dorm and lake be D

Since speed from dorm to lake is 30 mph, then time to get to lake =

Since speed from lake to dorm is 48 mph, then time to get to dorm =

Now, since it takes 12 more minutes to get from the dorm to the lake than it takes to get from the lake to the dorm, then it takes of an hour, or of an hour more, and we therefore have:

8D - 48 = 5D ------- Multiplying by LCD, 240

8D - 5D = 48

3D = 48

= miles

Therefore, the dorm and the lake are miles apart.
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