Crazy Algebra Question?

Question

A plane leaves going 200 mph. Another plane leaves 2 hrs later traveling 500 mph. How far from the starting points will the 2 plane converge? Show work.

Yeah, thats what I thought too. I am not looking for time, but the number of miles from the original starting point.

Answer 1

They will converge after x miles
X=200t =500(t-2)
300t = 1000
t= 3.33 hour
x= 200 *3.33 = 666.66 mile

Answer 2

If t is the duration (in hours) needed by the 500 mph plane to catch the 200 mph one and having in mind that the two planes will be at the same distance of the starting point, then one have the equation
200 * (t + 2) = 500 t
300 t = 400
t = 4/3 h or 1 hour and 20 minutes.

The distance is 500 mph * 4/3 h = 666.66 m

Answer 3

When the second plane takes off, how far has the first one travelled? Now, if we say that t is the time it takes after the second takes off before they converge, can you write an expression for the distance the first plane travels before they converge? Can you write an expression for the distance the second plane travels before they converge? Since they both travel the same distance, set the expressions equal to each other and solve for t. Then, you can find the distance.

First plane: 200t + (distance travelled in 2 hours)
Second plane: 500t

The answer is 666 2/3 miles.

Answer 4

So the first plane is already 400 miles out when the second plane leaves. After the first plane is 3 hours out it has traveled 600 miles and the second plane 500 miles, so lets see, one carry the three, yup it would be @ 666.6 miles plane two passes plane one 3 hours and 20 min after plane 1 leaves

Answer 5

converge is not the right term if one is catching up with the other, "catch up" is.

anyway

first plane's position, x1, is given by x1=200*t

where t is time, and 200 is its speed

2nd plane's position, x2, is x2=500*(t-2) where it is time (minus 2 because it leaves 2 hours later, positions defined only for 2 larger than 2).

so now you want both to be at the same point, so x1 = x2

200*t = 500*(t-2)

divide by 100
2*t = 5*(t-2)

develop
2*t=5*t-10

subtract 2*t from both sides, add 10 on both sides
10=3t

so t=10/3=3.333 hours, i.e. 3 hours and 20 minutes


BUT you're looking for the DISTANCE.

so now plug in this value of t into either equation for the position, say that for x1:
xm=200*(3.333)=666.667 miles
(xm is for "x meet")

to verify, plus the 3.333 hours into the equation for x2, you get:
xm=500*(3.333-2)=666.667 miles

so it works out indeed


hope this helps

Answer 6

Let

t = time fpr the first plane

t - 2 = time of the second plane

200 = speed of the first plane

500 = speed of the second

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

200t = 500(t - 2)

200t = 500t - 1000

200t + 1000 = 500t - 1000 + 1000

200t + 1000 = 500t

200t + 1000 - 200t = 500t - 200t

1000 = 300t

1000/300 = 300t/300

3.333333333 = t

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

multiply 60 minutes times the decimal

60 x 0.333333333 =19.99999999

or 20 minutes

- - - - - - - - - - -

The two planes converge 3 hours 20 minutes

200 x 3.33333333 = 666.66666666 Miles

Or 666.66 Miles rounded to two decimal places.



- - - - - - - - - -s-

Answer 7

very nicely, i'm a sprint rusty right here, so do no longer take my answer for the completed reality. So for the triangle, i think the width=base. the component to a triangle is (length cases width) cases a million/2, by using fact's a million/2 a sq.. 6cm squared= x cases 3cm. 4 cases 3 is 12, divide by potential of two, you get 6. The length is 4 cm. the fringe of the triangle might use the Pythagorean theorem. a squared + b squared = c squared, the place a and b represent the two sides, and c is the hypotenuse, or the side opposite of the desirable perspective. 4 squared + 3 squared, so sixteen+9=25. yet... we nonetheless ought to sq. root that because its c squared nonetheless, so the hypotenuse is 5. the completed perimeter could be 12. Now i'm uncertain with regard to the circle, i think it is related to the side that we merely discovered the dimensions for, the hypotenuse. If that's a a million/2 circle, then the line that it is related to is it is diameter, or the full length, side to side. The radius of a circle is a million/2 the diameter, or d=2r. by using fact the diameter, or as we pronounced previously, the hypotenuse, is 5cm long, then the radius could be 2.5 because 5/2=2.5cm. i'm hoping I helped. :)

Answer 8

Let the 2 planes converge in time t
It means that after time t hrs. both have travelled same distance(let it be d miles)

=>200t=d..................(1)
(t-2)500=d.................(2)

Substituting value of d form (1)
(t-2)500=200t
=>500t-1000=200t
=>t=1000/300=10/3 hrs
=>d=200*10/3=666.67 miles

Answer 9

m = miles
h = hours
200 m / h x 2 h = 400 m
Let X be the time it takes for the two to converge.
400m + 200mph(X) = 500mph(X)
400m = 300 mph (X)
X = 4 / 3 hr or 80 minutes.

Answer 10

3 hours 20 minutes