Question 147045
Problem 1

The simple formula below will help us solve the question :

distance = speed X time

The first average speed is = 105km/hr
Let us assume the duration the plane traveled at this speed to be x

The second average speed is =115km/hr
Let us assume the duration the plane traveled at this speed to be y

Now since we know that the total time taken was 5 hrs then the following must be also true :
x + y = 5
From this we can get :
y = 5 -x

Problem 2

Let us assume the speed of the bus to be x
The speed of the car is then = 2x - 30
Distance traveled = speed X time
So, distance traveled by car in 2 hours = 2(2x-30)
And distance traveled by bus = 2 X x = 2x
Now the distance traveled by car is 20 miles more so it means if we add 20 to the distance traveled by bus which is 2x then the distance traveled should be the same.  So we can say :
2x+20 = 2(2x-30)
2x+20=4x-60
2x-4x=-60-20
-2x=-80
2x=80
x=80/2
x=40
x is the speed of the bus so now we can say that the speed of the bus is 40km/hr.
Speed of car = 2x-30
=2(40)-30
=80-30
=50

Answer: The average speed of the car is 50km/hr.

Now, distance traveled is 555 km and there are two different speeds at which the plane traveled.
The distance covered by traveling at 105km.hr = speed X time = 105x
The distance covered by traveling at 115km.hr = speed X time = 115y
Total Distance = 105x + 115 y
Now since we are already given the distance we get the following :
555 = 105x+115y
We have previously found out that y=5-x, so we can substitute it in the above equation to get :
555 = 105x + 115(5-x)
555 = 105x + 115x5 - 115x
555 = 105x - 115x + 575
555 = -10x + 575
555-575 = -10 x
-20 = -10x
10x = 20
x=20/10
x=2
Now y = 5-x  =5-2 = 3

Ans.: The plane traveled at the speed of 105 km/hr for 2 hours(the value of x) and at the speed of 115km/hr for 3 hours(the value of y)

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