Question

Math question - matt and Kim are running to get in shape for sports. During the week they were in the loop that starts and finishes at the school. Matt runs the loop for six days and takes a 3 1/2 mile run on Sunday. Cameron salute for five days. He also runs 2 1/2 miles on Saturday and three and three-quarter miles on Sunday. They both are in the same number of miles during the week. How long is the loop they run at school?

Answer 1

The loop they run at school is 2.75 miles

Explanation:

Let's assume that the loop in the school is x miles long.

(a) Matt runs the loop for six days, therefore the distance covered by Matt during the six days is 6x miles.

on the seventh day which is on Sunday, he runs
`3(1)/(2) =3.5` miles

Therefore the total distance covered by Matt = (6x + 3.5) miles

(b) Cameron runs the loop for five days, therefore the distance covered by Cameron during the six days is 5x miles.

on the sixth day which is on Saturday, he runs
`2(1)/(2) =2.5` miles

on the seventh day which is on Sunday, he runs
`3(3)/(4) = 3.75` miles

Therefore the total distance covered by Cameron = (5x + 2.5 + 3.75) = (5x + 6.25) miles

Since they both run the same number of miles during the week,

⇒ 6x + 3.5 = 5x + 6.25

6x - 5x = 6.25 -3.5

`x = 2(3)/(4)=2.75` miles

The loop they run at school is 2.75 miles