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There was heavy traffic on the way there, and the trip took 6 hours. When Rita drove home, there was no traffic and the trip only took 4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Rita live from the mountains?
Do not do any rounding.



Answer :

mathstudent55

Answer:

264 miles

Step-by-step explanation:

distance one way from home to mountains = d

time to go from home to mountains = t_1 = 6

time to go from mountains to home = t_2 = 4

average speed on the way to mountains = s_1

average speed on the way home = s_2

speed = distance/time

Driving to the mountains:

s_1 = d/t_1

s_1 = d/6

Driving home:

s_2 = d/t_2

s_2 = d/4

Relationship of average speeds:

s_2 = s_1 + 22

s_1 = d/6

s_2 = d/4

s_2 = s_1 + 22

s_1 = d/6

s_1 + 22 = d/4

6s_1 = d

4s_1 + 88 = d

6s_1 = 4s_1 + 88

2s_1 = 88

s_1 = 44

The average speed on the way to the mountains was 44 mph.

distance = speed × time

d = s_1 × t_1

d = 44 × 6

d = 264

Answer: 264 miles

Check:

On the way to the mountains, it took her 6 hours.

264 miles / 6 hours = 44 mph

On the way back, it took her 4 hours.

264 miles / 4 hours = 66 mph

66 mph is indeed 22 mph faster than 44 hph.

Our answer is correct.

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