Q2. Distance Formula

Bob walks up and down a hill to get to school. He walks at 3 miles per hour up a hill and 4 miles per hour down a hill. The hill is 1 mile upwards and 1 mile downwards. What is his average rate?

Explanation

Key: You can’t sum up 3+4 for the rate and 1+1 for the distance. You need to treat these as two different trips.

You have two trips. You know the total distance. You are asked for the rate. That means you need to figure out how much time the trip took.

Trip 1 (up hill):

D = 1 mile

R = 3 miles / hour

Use D = RT

1 = 3(T)

T = 1/3 hour

Trip 2 (down hill):

D = 1 mile

R = 4 miles / hour

Use D = RT

1 = 4(T)

T = 1/4 hour

Total

D = 1 + 1 = 2 miles

T = 1/3 + 1/4 = 7/12 hour

D = RT

2 = 7/12 (T)

R = 24/7 miles / hour = 3.43 miles per hour

Source of question: Dr. Jang’s SAT 800 Math Workbook

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