Question

Josh drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Josh 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 Josh live from the mountains?

a) 320 miles
b) 360 miles
c) 400 miles
d) 440 miles

Answer 1

Josh lives 360 miles away from the mountains.

Step-by-step explanation:

To find the distance that Josh lives from the mountains, we need to determine his average speed on both trips. Let's call the distance he lives from the mountains 'd'. On the way there, the trip took 9 hours and his speed was 'x' miles per hour. So, the equation to represent this is d = 9x. On the way back, the trip took 4 hours and his speed was 'x + 40' miles per hour (because he was 40 miles per hour faster on the way back). So, the equation to represent this is d = 4(x + 40). We can solve these equations to find the value of 'd' by setting them equal to each other: 9x = 4(x + 40). Solving for 'x', we get x = 40. Substituting this back into one of the equations, we find d = 9(40) = 360 miles. Therefore, the answer is option b) 360 miles.