Math question:?

Question

Romeo and Juliet saw each other when they were 270 feet apart. Romeo began running toward Juliet at a rate of 16ft/sec. At the same moment, Juliet began running toward Romeo at the rate of 14ft/sec.

How many secods after they started running will they meet?

How far will Romeo have run then?

Thank you!!!!!!

Answer 1

Nine seconds.

Their relative speed is 30 feet per second. 270/30=9.

Romeo will have run 144 feet (9*16).

Of course this assumes they had instantaneous acceleration, and doesn't take into account that they would collide at an average speed of fifteen feet per second if they didn't decelerate. Not very romantic.

Answer 2

Since they run at each other, they are closing the interval at 16+14 ft/sec or 30 ft/sec. Then they will meet after 9 seconds. Romeo will have run 16*9 feet=144 ft.

Answer 3

s = no. of seconds

How many secods after they started running will they meet?
16s + 14s = 270
30s = 270
s = 9

Answer: 9 seconds

Proof:
270 - 9(16) - 9(14) = 0
270 - 144 - 126 = 0
0 = 0

How far will Romeo have run then?
= 9 * 16
= 144

Answer: 144 feet

Answer 4

let the time taken to meet = t sec

distance travelled by Romeo = 16 t ft (speed *time)

distance travelled by Juliet = 14 t ft

16 t + 14 t = 270

30 t = 270

t = 270/30

= 9 sec

romeo travelled (9*16) = 144 ft

Answer 5

In 1 second, both have traveled 30 feet. In 9 seconds, they have traveled 30x9=270 feet.

Answer 6

Ok... let's see...
The ecuations for this problem are:
Xf(R)=Xo(R)+Vo(R)T --> For Romeo
Xf(J)=Xo(J)+Vo(J)T --> For Juliet

Xf is final position, Xo is initial position, Vo is the velocity...

So, when they meet the final meet they'll be in the same final position: Xf(R)=Xf(J)=Xf
Then,
Xo(J) - Vo(J)t = Xo(R) + Vo(R)t
Vo(R)t + Vo(J)t = Xo(J) - Xo(R)

t = [Xo(J) - Xo(R)] / [Vo(R) + Vo(J)]
t = 9 seconds

Now, to calculate how far Romeo will be:
Xf = Xo(R) + Vo(R)t {knowing that t = 9 sec}
Xf = 144 ft.