Question

Shen drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Shen drove home, there was no traffic and the trip only took 4 hours. If his average rate was 40 miles per hour faster on the trip home, how far away does Shen live from the mountains?

Answer 1

288 miles

Step-by-step explanation:

Time taken with traffic = 9 hours

Time taken without traffic = 4 hours

Speed with traffic = x mph

Speed without traffic = x+40 mph

Distance = Speed × time

Distance travelled in 9 hours

9x

Distance travelled in 4 hours

4(x+40)

Since both the distances are same

`9x-4(x+40)=0\\\Rightarrow 9x-4x-160=0\\\Rightarrow 5x-160=0\\\Rightarrow x=(160)/(5)\\\Rightarrow x=32\ mph`

Speed with traffic = 32 mph

Distance travelled = 9×32 = 288 miles

∴ Shen lives 288 miles from the mountains