Algebra (Basic) Help - just checking? ?

Question

A car enters an interstate highway 15 mi north of a city. The car travels due north at an average speed of 62.5 mi/h. Write an equation to model the car's distance, d, from the city after traveling for h hours. Graph the equation.

My work: d=62.5h-15

AND

A pump removes 1000 gal of water from a pool at a constant rate of 50 gal/min.

a. Write an equation for the amt. of water y in the pool after t minutes.

b. Determine t- and y- intercepts.

My work:

a. y=50t-1000

b. y-int.=-1000

t-int=20

I'm having some doubts just because my math sense is a little off...

Thank you in advance - please explain any errors! :)

Answer 1

General form for regular linear motion is

d = vt + d0

d0 is the initial distance, that is the distance when t = 0. It is 15 miles north, or + 15 miles if northward direction is taken as positive. In that case the speed pointing north is + 62.5 miles/hr and the equation given the dependence of d on t is

d = 62.5t + 15

in which d is in miles and t is in hours.

General form of the equation describing the dependence of the volume of water in the pool on time

V = vt + V0

V0 is the initial volume, equal to +1000 gallons.

The speed at which the water is pmped out is 50 gallon/min.  Since that speed tell how much water in the pool decreases per minute , it should take negative sign. So v = -50 gal/min

V=-50t + 1000

(V in gallon and t in minute)

V = 0 as t = 100/50 = 20 min

t = 0, V = V0 = 1000 gallon.

Answer 2

d=62.5h-15

Not correct.  Since the car enters 15 miles North of the

city and is traveling further north, the start point is

Positive 15 so d = 62.5h + 15 , not minus 15

*I'm not sure if it's...

y=50t+1000

or y=50t-1000    ANSWER IT IS NEITHER OF THESE

Since 1000 gallons is the amount of water removed

note that it is +1000 to begin, then as water is removed

it is taken away from the thousand gallons.  Take away

in math is modeled by the minus sign, not the  plus so

it would be 1000 - 50t which could be written as

-50t + 1000

Your part b work would be right if you had done part

a right.  In fact your t intersept is correct , it is 20

because you have two sign mistakes that cancel.  

Of course the correct y intercept is  1000

Answer 3

according to me,

d=62.5h+15

15 miles is added as the car enters the highway north of the city and travels north thus increasing its distance from the city.

And

y=1000-50t

1000gal is the maximum amount of water that the pump removes