Question

Ben walks at a rate of 3 miles per hour. He runs at a rate of 6 miles per hour. In 1 week, the combined distance he walks and runs is 210 miles.

Write a linear model that relates the # of hours Ben runs.
Ben runs for 25 hours. For how many hours does he run?

Answer 1

he runs 150 miles as 6*25 equals 150 miles

Answer 2

-- Ben walks at a rate of 3 miles per hour. If he walks for 'W' hours,
then the distance he covers in that time is 3W miles.

-- Ben runs at a rate of 6 miles per hour. If he runs for 'R' hours,
then the distance he covers in that time is 6R miles.

If he does some running and some walking during the week, then
we might not know how many hours he walked and how many hours
he ran, but we can be sure that the total distance he covered is

Total D = 3W + 6R .

-- If the total distance is 210 miles,and he ran for 25 hours, then

210 = 3W + 6(25)

210 = 3W + 150

Subtract 150 from each side: 60 = 3W

Divide each side by 3 : 20 = W

He walked for 20 hours during the week.

Check:

Running hours: R=25, Running D = 6R = 150 miles.

Walking hours: W = 20, Walking D = 3W = 60 miles.

Total distance = 150 miles + 60 miles = 210 miles yay !