SOLUTION: On Monday, the Davis family left home to drive to a resort in California for vacation. They drove at an average rate of 48 miles per hour. On Saturday, they drove back the same rou

Algebra ->  Inequalities -> SOLUTION: On Monday, the Davis family left home to drive to a resort in California for vacation. They drove at an average rate of 48 miles per hour. On Saturday, they drove back the same rou      Log On


   

Question 1101219: On Monday, the Davis family left home to drive to a resort in California for vacation. They drove at an average rate of 48 miles per hour. On Saturday, they drove back the same route, traveling at an average rate of only 32 miles per hour because of road construction. If the Davis family spent a total of 10 hours driving to and from the resort in California, how many miles did they travel from their house to the resort?
A.192 mi
B.84 mi
C. 160 mi
D.400 mi
Found 3 solutions by richwmiller, ikleyn, greenestamps:
Answer by richwmiller(17219) About Me  (Show Source):
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If they traveled the whole trip at 32 mph, they would travel 320 miles 32*10=320
If they traveled the whole trip at 48 mph, they would travel 480 miles 48*10=480
So it is somewhere in between 320 and 480. but we want only one way
Which of the choices is BETWEEN 160 and 240? It can't be 160. 192 looks good.
32/48=2/3
2x+3x=10
5x=10
x=2
2x=4
3x=6
6 hours at 32 6*32=192
4 hours at 48 4*48=192
So it is indeed 192

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let D be the distance from their home to the resort, in miles.


The way from the home to the resort at 48 mph took  D%2F48  hours  (time = distanse%2Fspeed).

The returning trip at 32 mph took  D%2F32  hours.


As the condition says, the two-ways trip took 10 hours, in all.

It gives you an equation

D%2F48 + D%2F32 = 10.


To solve it, multiply both sides by 96  (which is less common multiple of the numbers 48 and 32). You will get

2D + 3D = 96*10  ====>  5D = 960  ====>  D = 960%2F5 = 192.


Answer.  The one way distance is 192 miles.


Check.   192%2F48 + 192%2F32 = 4 + 6 = 10 hours.  ! Correct !



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The ratio of the two speeds is 48:32, or 3:2.

Since the distances are the same, the ratio of times spent at the two speeds is 2:3.

If the total driving time was 10 hours, then they spent 4 hours at the higher speed and 6 hours at the lower speed.

4*48 = 192; 6*32 = 192.

The distance from their house to the resort was 192 miles.