Question

2. of a certain journey is covered at the rate
of 25 km/h, at the rate of 30 km/h and the
5.
4.
h
rest of 50 km/h. What is the average speed
for the whole journey? UNV 2017, 2009)
1
(1) 30 km/h (2) 33 km/h (3) 33 km/h (4) 32 km/h
3.​

Answer 1

Formula: Speed = Distance/ Time, Therefore, Time = Distance / speed

Given that speed of the car is 20km/hr more than the average speed of the bus, Let the speed of the bus be x,

Therefore speed of the car is x+20.

Average speed of the bus:

300/x - 4=300/x+20

=> 300[x+20-x/x(x+20)]= 4

=> 300(20/ x(x+20)) = 4

=> 300(20/x²+20x) = 4 (upon cross multiplying)

=> 6000= 4x²+80x

4x²+80x-6000=0

4(x² + 20x -1500) =0

x²+20x-1500=0

Upon factorizing,

(x+50)(x-30)=0

x=30

The bus goes 30 kmph; the car goes 50 kmph