At what time will the two planes be if they are 450 km apart?

Question

Two planes leave the airport at 8 am and travels in the same direction. Plane A travels 960 kph while Plane B at 810 kph. At what time will the two planes be if they are 450 km apart? Show solution. Another question. Two buses left a gasoline station at the same time and travel in opposite directions. Bus A travels 80 kph while Bus B travels 108 kph. After how many hours will the two buses be 329 km apart? Show solution

Answer 1

We can find the difference in speed of the planes: 960-810=150kph. Now we find out how long at that speed it will take to travel 450km=450/150=3 hours. So they would be 450km apart at 11am.

Their relative speed is 108+80=188kph. To travel 329km at 188kph takes 329/188=1.75hr or 1hr 45min.

 

Answer 2

Question 1 is unclear to me, so I assume you want to say that the planes leave from same airport and you want to find the time when they are 450 kms apart.

Solution 1)

Let t be the time required for these two plane be 450 kms apart.

So distance (x) travelled by plane A in t hours = 960t  (since distance = speed * time)

and distance (y) travelled by plane B in t hours = 810t

Given, plane A is 450 kms ahead of plane B in t hours.

So, x = y + 450

=> 960t =810t +450

=> 960t - 810t = 450

=> 150t = 450

=> t =450/150 = 3 hours

So it will take 3 hours for plane A to get 450 kms ahead.

Solution 2)

Distance travelled by bus A be x in t time.

Distance travelled by bus B be y in t time.

x = 80t

y = 108t

Given, they are moving in opposite direction so sum of the distance should be equal to 329km at time t.

x + y =329

=> 80t + 108t = 329

=> 188t = 329

=> t =1.75 hours

or t = 1 hour 45 minutes

or t = 105 minutes