Question

A yellow hot-air balloon is 100 feet off the ground and rising at rate of 8 feet per second.An orange hot-air balloon is 160 feet off the ground and rising at a rate of 5 feet per second. After how long will the Yellow balloon be higher than the orange balloon?

Answer 1

ANSWER

Find out the how long will the Yellow balloon be higher than the orange balloon.

To proof

Now  the diagram is given below

As given

A yellow hot-air balloon is 100 feet off the ground and rising at rate of 8 feet per second.

i.e height of the yellow baloon off the ground  = 100 feet

rising at rate = 8 feet per second.

.An orange hot-air balloon is 160 feet off the ground and rising at a rate of 5 feet per second.

i.e height of the orange baloon off the ground  = 160 feet

rising at rate = 5feet per second.

Formula

$Relative\ velocity = \frac{Relative\ Distance}{Relative\ time}$

Relative velocity =  rising rate of yellow balloon -   rising rate of orange balloon

= 8 -5

= 3 feet per second

Relative distance =  height of the yellow baloon off the ground -  height of the orange baloon off the ground

= 160 -100

= 60 feet

put in the formula

$= \frac{60}{3}$

= 20 second

after  20 second Yellow balloon will be higher than the orange balloon.

Hence proved