Question

The receivers for the Dayton University football team are practicing running different routes on the field. They have to run a specific distance so that the quarterback knows exactly where to throw the ball. Duncan ran 25 post routes and 16 slant routes, which meant he ran a total of 462 yards. Finn ran 20 post routes and 16 slant routes, which equaled a total of 392 yards. How long is each route?

A) Post route: 16 yards, Slant route: 25 yards
B) Post route: 25 yards, Slant route: 16 yards
C) Post route: 21 yards, Slant route: 14 yards
D) Post route: 20 yards, Slant route: 16 yards

Answer 1

The problem involves solving a system of linear equations using algebra to find the lengths of the post and slant routes. However, upon solving, we find that the post route is 14 yards and the slant route is 7 yards, which does not match any of the answer choices provided. Thus, we suggest verifying the values given in the question.

Step-by-step explanation:

The question involves solving a system of linear equations to find the length of each type of football route run by the players. Let's use algebra to find the length of the post route and the slant route.

Let x be the length of a post route and y the length of a slant route. According to the information given:

• For Duncan: 25x + 16y = 462
• For Finn: 20x + 16y = 392

Subtract the second equation from the first to get:

5x = 70

Dividing both sides by 5, we find:

x = 14 yards (post route)

Plug the value of x into one of the equations to find y:

20(14) + 16y = 392

280 + 16y = 392

16y = 112

y = 7 yards (slant route)

However, these lengths do not match any of the answer choices, which means there might be a mistake in the question. The student should verify the numbers provided or the question might be incorrect as proposed.