David knew he made a mistake when he calculated that gilda walks 123 miles to the station. read through david's calculations: using d = rt, the distance is the same, but the rate and time are different. if gilda misses the train, it means the time t needs 7 more minutes at a rate of 3 mph, so d = 3(t + 7). if she gets to the station 5 minutes early it means the time t can be 5 minutes less at a rate of 4 mph so d = 4(t - 5). 3(t + 7) = 4(t - 5) 3t + 21 = 4t - 20 t = 41 d = rt, so d = 3(41) = 123 find david's mistake in his calculations. in two or more complete sentences, explain his mistake. include the correct calculations and solutions in your answer.

d= 3(t + 7) (1)

d= 4(t- 5)(2)

3(t + 7) = 4(t - 5)

3t + 21 = 4t - 20

t = 41

For finding the Distance to the station, we need to use either equation (1) or (2). Here two different rates are given 3 mph and 4 mph. So, we can't consider r= 3 only.

If we use the equation (1), then

d= 3(t + 7)

d= 3(41 +7)

d= 3(48) = 144

We can also use the equation (2)

d = 4(t - 5)

d= 4(41- 5)

d= 4(36) = 144

So, the correct distance to the station is 144 miles.

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)