Confusing ALGEBRA word problem 2?

Question

A person orders a TAXI to take her to the airport.
---If the taxi is driven at 80km/h she will miss her flight by 2mins (1/30 of an hour)
--If the taxi is driven at 90km/h she wll make the flight with 1min(1/60 of an hour) to spare.

Write down an equation and solve it to WORK OUT HOW FAR SHE LIVES FROM THE AIRPORT.

Please put in some explanations to help me understand. Thank you.






Answer:
36km.

Answer 1

The general formula is rate * time = distance. (rt=d)

I am going to use t = d/r. t = time it takes to get there exactly on time.

In the first case, d/80 = t + 1/30
Solve for t, you get t = d/80 - 1/30

In the second case, d/90 = t - 1/60
Solve for t, you get t = d/90 + 1/60

Set those equal to each other and solve for d:

d/80 - 1/30 = d/90 + 1/60
-1/60 - 1/30 = d/90 - d/80
-1/20 = 80d/7200 - 90d/7200
-1/20 = -10d/7200
-360 = -10d
36 = d

Answer 2

It starts out simple and the fractions make it harder.

distance = rate * time

Eq 1, d= 80 km/hr * (t + 1/30)
Eq 2 d = 90 km/hr * (t - 1/60) the distance is the same, the time part is how long it took you to get to the air port

set eq1 = eq2

so 80 * (t + 1/30) = 90 * (t - 1/60) I am going too skip some steps, you can work on simplification

80t + 80/30 = 90t - 90/60 we solve for t

10t = 80/30 + 90/60
t= 125/300 hrs

plug in to equation 1

d = 80 * (125/300 + 1/30) do the math d= 36 km

Answer 3

Let x = length of side of cube. Then we have: x³ = 2(x+2)(x-4)(x-1) - 48 which is what the problem states, if you read this carefully. Now, we expand the right side to get: x³ = 2 x³ - 6 x² - 12 x + 16 - 48 Rearranging and cleaning up a little bit, we have: x³ - 6 x² - 12 x - 32 = 0 which factorizes into: (x - 8)(x² + 4x + 4) = 0 So that the answer is x = 8, and the dimensions of the rectangular box is 10, 4, and 7, having a volume of 280. The volume of the cube is 512, which is 2(280) - 48

Answer 4

Now in the first case, the speed(v) is 80km/hr and time(t) is unknown all we know that it is the real time + 2 mins late.
Therefore we have the speed formula
v= d/t
t=v/d
where v= 80
t= t +1/30 (we have to convert to hrs because speed is in
hrs)
d=??
Therefore:
t+1/30 = 80/d
t= 80/d - 1/30
Now this is your first equation.

Second equation: we know v=90, t= t -1/60 where t is the real time it takes to the airport and we subtract it from the 1 minutes as she arrived early by one min.
Now you do the same thing you did in the first equation you fill in the speed formula :
v=d/t
t= d/v
t-1/60 = d/90
t = d/90 + 1/60
this is your second equation.
Now first equation = second equation , they both represent the real time it takes to get to the airporrt.

:. t = d/80 - 1/30 = d/90 + 1/60
Now all you have to do is work out d the distance.
d/80 - 1/30 = d/90 + 1/60
d/80 - d/90 = 1/60 + 1/30
(90d - 80d) /7200 = 0.05
10d/7200 = 0.05
10d = 0.05 x 7200=360
d = 360/10
d = 36km. This is your final answer.

Answer 5

This problem involves distance, rate and time

The formula is d = rt.

d = rt

d/r = t. . . use this formula

d = distance
80 = Rate
t + 1/30 = Time
90 = rate
t - 1/60 = time

- - - - - - - - -

The formula for time

d/80 = t + 1/30. . .Transposing 1/30

d/80 - 1/30 = t + 1/30 - 1/30

d/80 - 1/30 = t. . . first equation

- - - - - -

d/90 = t - 1/60

d/90 + 1/60 = t / 160 + 1/60

d/90 + 1/60 = t. . . .second equation

- - - - - - - - - - - -

d/80 - 1/30 = d/90 + 1/60

d/80 - 1/30 - d/80 = d/90 + 1/60 - d/80

- 1/30 = d/90 + 1/60 - d/80

- 1/30 - 1/60 = d/90 + 1/60 - d/80 - 1/60

- 1/30 - 1/60 = d/90 - d/80

- 720(1/30) - 720(1/60 = 720(d/90) - 720(d/80)

- 24 - 12 = 8d - 9d

- 36 = -d

- 1(- 36) = -1(- d)

36 = d

- - - - - - - - -s-

Answer 6

let's t the time she needs exactely to take the flight and d distance of the airport , since d = vt where v is the speed by hour

you can write
d= 80(t+1/30) (1)
and also d= 90(t-1/60) (2)

so 80t +80/30= 90t -90/60
10t = 8/3+9/6= 25/6 so t = 25/60inhour

and you replace t by its value in one of the equations you found 36 km

Answer 7

If the distance is 1 km,time taken@80Kmph=1/80 hrs
and time taken @90KmPh is 1/90 hrs
Difference of time=1/80 - 1/90 =1/720 hr
Actual difference of time=1/30 +1/60 =1/20 hrs
(1/30 hr late and 1/60 hr earlier makes a difference of 1/30 +1/60)
If the difference of time is 1/720 hr, the distance is 1 km
Therefore if the distance is 1/20 hr.the distanceis
(1/20)/(1/720)
=36 Km

Answer 8

using V = D / T
t+2 = D/80
and t-1 = D/90
=> t+2/(t-1) = 9/8
8t + 16 = 9t - 9
or t = 25min = 25/60hr
D = (t-1)*90 = 24*90/60 = 36km

Answer 9

This is a [distance] = [rate] * [time] problem.

t = time to airport at 80 km/hr

time to airport at 80 km/hr - time at 90 km/hr
= 2 - (-1) = 3 min = 1/20 hr

t - 1/20 = time to airport at 90 km/hr
d = distance to airport

d = 80t = 90(t - 1/20) = 90t - 90/20
90/20 = 10t
9/20 = t

d = 80t = 80(9/20) = 36 km