SOLUTION: Martina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Martina drove home, there was no traffic and the trip only

Question 1056999: Martina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Martina drove home, there was no traffic and the trip only took 7 hours. If her average rate was 18 mph faster on the trip home, how far away does Martina live from the mountains?
Found 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
Martina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours.
When Martina drove home, there was no traffic and the trip only took 7 hours. If her average rate was 18 mph faster
on the trip home, how far away does Martina live from the mountains?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let "u" be Martina's average speed on the way from home to mountains (in miles per hour). Then in this way she covered the distance of 10*u miles. On the way back her average speed was (u+18) mph, according to the condition. And the way back was 7*(u+18) miles long. Actually, both the ways are equally long, which gives an equation 10u = 7(u+18). Simplify and solve for u: 10u - 7u = 7*18, 3u = 7*18, u = 7*6 = 42. Thus Martina's speed was 42 mph on the way to mountains. Hence, the distance to mountains is 10*42 = 420 miles.

Solved.

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Another one of those specific types of constant travel rate problems, so this will be all in variables.

RATE or SPEED TIME DISTANCE GOING TO r h d RETURNING r+k p d

Question essentially asks for d.
--------this is the system to solve.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Martina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Martina drove home, there was no traffic and the trip only took 7 hours. If her average rate was 18 mph faster on the trip home, how far away does Martina live from the mountains?

With D being the distance, the SPEED equation you need is:
7D = 10D - 1,260 ----- Multiplying by LCD, 70
7D - 10D = - 1,260
- 3D = - 1,260
D, or distance =
See how easy that was? Nothing complex!!
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