Question

A small plane travels north at 240 mph. A jet leaves the same airport 30 minutes later and follows the other plane at 360 mph. How long does it take the jet to take over the other small plane? what distance are they from the airport?

SHOW ALL YOUR EQUATIONS.

Two cars start at the same point and travel in the same direction on the same road. one travels 50 kmph and the other 45kmph. After how many hours will they be 20km apart?

SHOW ALL YOUR EQUATIONS, USE ALGEBRAIC EQUATIONS.

Thank you!

Answer 1

1.

Solution here,

let the both planes covers same distance x while over taking.

For the small plane, let time be t.

speed= 240 mph

now,

distance covered by it,

x=240t--------(1)

For jet plane,let the time be t'.

speed=36mph

since it is flewed after 30 mins, it can be written as,

t'=t-30 min=t-0.5 hr

now distance covered by it,

c=360t'=360(t-0.5)=360t-180----------(2)

equating (1) and (2)

240t=360t-180

or, -120t=-180

or, t=1.5 hr

therefore two planes wiil meet after 1.5 hrs.

putting the value of t in (1)

x=240×1.5=360 m

therefore they travel through 360 m from the airport whlie over taking.

2.

For the first car,

speed=50 Kmph

let it covers x distance at time t

so,diatance x=50t--------(1)

For the second car,

speed=45 Kmph

according to the question, in time t, it will covers the distance (x-20)Km

so, distance(x-20)=45t

or, x=45t+20---------(2)

equating (1) and (2),

50t=45t+20

or, 5t=20

or, t=4 hrs.

therefore cars will be apart of 20 km after 4 hrs.