Martina drove to the mountains last weekend.

Question

Martina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 

 hours7. When Martina drove home, there was no traffic and the trip only took 4  hours. If her average rate was 

 27 miles per hour faster on the trip home, how far away does Martina live from the mountains?

Do not do any rounding.

Answer 1

Hi Solita,

Your Question: Martina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took  hours7. When Martina drove home, there was no traffic and the trip only took 4 hours. If her average rate was  27 miles per hour faster on the trip home, how far away does Martina live from the mountains? Do not do any rounding.

Given: Round trip to mountains. Way there 7 hours, Way back 4 hours. Rate on way home 27 mph faster

Let

t₁=time there = 7 hours

t₂= Time home = 4hours

v₁= Velocity (Rate) there

v₂= Velocity home = Velocity there plus 27 = v₁ + 27mph

d₁= distance there

d₂= distance home

Find: How far does she live from the mountains.

The distance traveled is equal to the rate of travel x time.

d₁= v₁ × t₁ = v₁ x 7hours

d₂= v₂ × t_{2 =} v₂ x 4 hours = (v₁+27mph) x 4 hours

The distances are the same, so you can set the equations equal to eachother

d₁=d₂

v₁ x 7hours = (v₁+27mph) x 4 hours

7hours x v₁=4 hours x v₁ + 108miles

3hours x v₁= 108miles

v₁=36mph

Now that you know how fast the drive there was, you can calculate the distance

d₁= v₁ x t₁

d₁ = 36mph x 7 hours = 252Miles

You can check that this is correct by making sure the distance on the way back is the same.

v₂=v₁+27mph

v₂= 36mph + 27mph = 63mph

d₂= v₂*t₂

d₂= 63mph x 4 hours = 252 miles

Hope this helps :)