Quick Math Problem Help?

Question

Ok, normally I wouldn't do this, so don't give me any answers such as do your own homework or whatever.
I have tried this myself, I have been working on it for hours. My parents can't figure this out and either can my older sister.

I'm sure this is a simple problem, but I am very tired and need to get some sleep. I'm really not smart when it comes to math. I just need to get this done.

Problem:
Could somebody tell me how to do this?
Winona is meeting Karen's plane
If she goes 20 mph = 1 hr late
If she goes 40 mph = 1 hr early

How many miles away is the airport?

Btw, the answer is NOT 30. My teacher has already told me that.

Answer 1

Well you need a difference of two hours. 80 miles = 4 hours at 20 miles an hour and two hours at 40 miles an hour.

20 if the plane gets in at 8 and she leaves at 5 if she goes 20 miles an hour she will get there at 9 an hour late. If she goes 40 miles an hour she get there at 7 an hour early!

Answer 2

Okay, I'm going to think about this as I write and maybe you'll see my process. There is a two-hour difference between Winona going 20 mph and going 40 mph. If she was 40 miles away, she'd get there in one hour, but it would take two hours at 20 mph. That's only a 1 hour difference. So I guess TWICE as far: 80 miles. That would take two hours at 40 mph and four hours at 20, so that's the two-hour difference. She's 80 miles away. If she drove 30 mph, she'd be just on time. You can actually also tell from these numbers how long ahead of time she is going. 30 mph is one mile per two minutes, 80 times 2 says she's starting out 160 minutes before she's supposed to be there; 2 hours and 40 minutes. Did you see how that worked?
Better to be early. Could be traffic. Hope this helps.

Answer 3

Start with the formula velocity = distance/time or

v = d/t then rearrange to

d = vt

The distance is fixed... it's always the same distance to the airport from her house. Right?

Say she needs to get to the airport in t hours. Then 1 hr late would be t + 1 and one hour early would be t - 1 (plug in numbers to convince yourself if you aren't sure which one should be +1 and which should be -1). Then:

(20mph)(t+1hr) = (40mph)(t-1hr)



OK so now just distribute and solve the equation:

20(t+1) = 40(t-1)
20t + 20 = 40t -40
-20t = -60
t = 3 hrs
Remember we said t was the time it should take to drive. She actually drove t + 1 or 4 hrs at 20 mph or t - 1 or 2 hrs at 40 mph.

Now you need to figure out how far away the airport is using the formula distance = velocity x time.

You can use either 20mph x 4 hrs or 40 mph x 2 hrs and get the same distance.

You can also calculate how fast she *should* drive to get there on time by dividing the distance by 3 hrs. :-)

Answer 4

80 miles.

Say, t is the time it would normally take her. And, d is the distance.

In the first case, d = 20 * (t+1)
In the second, d = 40 * (t-1)

Equate the two: 20*(t+1) = 40*(t-1)
=> 40t - 20t = 40+20
=> t = 3.

Because you need the distance to the airport, put t=3 in one of the d equations.

d = 20*(t+1) = 20 * 4 = 80

Answer 5

Rags has the correct answer of 80 miles.
20 mph = 4 hours
40 mph = 2 hours
She needs to be there in 3 hours.

DON'T forget to give him the best answer

Answer 6

a million. 15 - x over 4 = -8 (15 - x) / 4 = -8 (15 - x) = -32 -(15 - x) = 32 x = 40 seven 2. what occurs if the 8 have been an excellent? 15 - x over 4 = 8? (15 - x) / 4 = 8 15 - x = 32 x = 15 -32 = -17 3. additionally handling percents! what would the p.c. enhance be? $50.00 is the unique value $80.00 is the recent value p.c. enhance = 60 4. discover the low-priced value 40 9.ninety 9 low-priced 25% 37.40 9

Answer 7

The time it takes to travel a set distance is equal to the distance divided by the speed:
T=D/S

Let us use units of miles and hours.

Traveling distance X at 20mph means you arrive 1 hour late, so:
T+1 = X / 20

Traveling 40mph you arrive 1 hour early, so:
T-1 = X/40

Rearranging you have:
T = (X/20) - 1 and
T = (X/40) + 1

Set equal to eachother and solve for X:
(X/20) - 1 = (X/40) +1
(X/20) - (X/40) = 2 set denominators to eachother
(2X/40) - (X/40) = 2
X/40 = 2
X = 80 miles

Answer 8

You need to use the formula Distance = Rate x Time.
Call the distance D and the correct time T.

From the first condition, we have D = (20) x (T+1). (You need one more hour of travel time than the correct time.)
From the second condition, we have D = (40) x (T-1). (You need one fewer hour of travel time than the correct time.

Then 20(T+1)=40(T-1). Solving for T, you get the correct travel time, and using that time, you can find the distance by plugging into either equation above.

Answer 9

80

Answer 10

80 miles

Make X = time at 40 mph then
X+2 = time at 20 mph so
40X = 20(X = 2)
40X = 20X + 40
40X - 20X = 40
X = 2

So 2 hours at 40 mph equals 80 miles and
4 hours at 20 mph also equals 80 miles.