Question

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

Answer 1

420 miles

Step-by-step explanation:

Since distance is speed times time taken, you get two conditions:

`\left \{ {{d=v*10} \atop {d=(v+18)*7}} \right.`

Easiest way to solve it is to set the two condition equal - she's coming and going from the same place after all - and you get
`10v=(v+18)*7\\10v=7v+3*6*7\\3v=3*6*7 \\v=42` Replace in either equation and you'll get
`d=420`