Question

One car moving on a straight road covers one third of distance with a speed of 20 m/s, other one third with speed of 40 m/s and next one third with speed 60 m/s, then the average speed of the car is:

Options

• 32.7 m/s

• 40 m/s

• 31 m/s

• 33 m/s

Answer 1

32.7 m/s

Explanation:

Average speed = `"Total distance"/"Total time"`

Total time is t₁ + t₂ + t₃

t₁ = `"x"/(3 xx 20)`, t₂ = `"x"/(3 xx 40)`, t₃ = `"x"/(3 xx 60)`

∴ Average speed = `"x"/("x"/(3 xx 20) + "x"/(3 xx 40) + "x"/(3 xx 60))`

= `"x"/("x"/3 (1/20 + 1/40 + 1/60))`

= `3/((9 + 4.5 + 3)/180)`

= `(3 xx 180)/16.5`

Average speed = 32.7 m/s

Short trick: Av. speed = `(3 xx 20 xx 40 xx 60)/(20 xx 40 + 40 xx 60 + 60 xx 20)`

= `(144000)/(800 + 2400 + 1200)`

= `144000/4400`

= 32.7 m/s