Question

Angelo runs 7 miles per week and increases his distance by 1 mile each week. Marc runs 4 miles each week ans increases his distance by 2 miles each week. In how many weeks will Angelo and Marc be running the same distance? What will that distance be?

Answer 1

At week 3 both Angelo and Marc will be running an equal distance of 10 miles

Solution:

Given that, Angelo runs 7 miles per week and increases his distance by 1 mile each week

Let "w" be the number of weeks

Let "d" be the total distance ran

Then by given statement,

total distance ran = 7 miles + 1 mile x (number of weeks)

d = 7 + w --- eqn 1

Marc runs 4 miles each week and increases his distance by 2 miles each week

total distance ran = 4 miles + 2 mile x (number of weeks)

d = 4 + 2w ----- eqn 2

Therefore, to find the number of weeks for which Angelo and Marc be running the same distance, equate both the distance

7 + w = 4 + 2w

Solve the above expression for "w"

7 - 4 = 2w - w

w = 3

At week 3 both Angelo and Marc will be running an equal distance

What will that distance be?

Subtitute w = 3 in eqn 1

d = 7 + w = 7 + 3 = 10

Thus, they will be running 10 miles at week 3