Question

Ivan drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Ivan drove home, there was no traffic and the trip only took 4 hours. If his average rate was 27 miles per hour faster on the trip home, how far away does Ivan live from the mountains? Do not do any rounding.

Answer 1

Answer:252 miles

Step-by-step explanation:

Given

During his way to mountain it took 7 hr to drive

and during his return trip it took 4 hr to return

Let x be the distance between home and mountain

average speed for return is 27 miles per hour faster than his former trip

let v be the speed on his way to mountain thus v+27 is his return speed

thus
`7=(x)/(v)`----1

for return trip

`4=(x)/(v+27)`-----2

divide 1 & 2

`(7)/(4)=(x\cdot (v+27))/(v\cdot x)`

`7v=4v+4\cdot 27`

`3v=4\cdot 27`

`v=36 mph`

thus
`x=7* 36=252\ miles`