Answer:
Question not completed, so I analysed the question first
Tony drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 6 hours. when tony drove home, there was no traffic and the trip only took 4 hours. if his average rate was 22 miles per hour faster on the trip home, how far away does tony live from the mountains?
Explanation:
Let use variables to solve the problems
Let the first trip to be mountain take x hours
Let the trip back home take y hours
Let the speed to while going to the mountain be a miles/hour
Then, while going home it was b miles/hour faster than while going to the mountain.
Then, speed going home is (a+b)miles / hour
The formula for speed is given as
Speed=distance/time
The constant through out the journey is distance, the two journey has the same distance.
Then,
Distance =speed×time
For first journey going to the mountain
Distance = a×x=ax miles
For the second journey going home
Distance =y×(a+b)
Distance Mountain= distance home
ax=y(a+b)
Make a subject of the formula
ax=ya+yb
ax-ya=yb
a(x-y)=yb
a=yb/(x-y)
Therefore, distance from mountain is
Distance=speed ×time
Distance= a×x=ax
Now, applying the questions
So from the questions
x=6hours, y=4hours
Also, b=22miles/hour
Then,
a=yb/(x-y)
a=4×22/(6-4)
a=88/2
a=44miles/hour
Then, the house distance from the mountain is
Distance=ax
Distance =44×6
Distance =264miles
