The average speed of a car running at 70 km/hr for 1 hour and ‘P’ km/hr for $1\frac{1}{2}$ hour is 55km/hr. Find the value of p

Speed₁ = 70 km/hr, Time₁ = 1 hour
Speed₂ = $P$ km/hr, Time₂ = $1\frac{1}{2} = \frac{3}{2}$ hours

Average speed = 55 km/hr

Average speed = Total distance ÷ Total time

Total distance

Distance₁ = $70 \times 1 = 70$

Distance₂ = $P \times \frac{3}{2} = \frac{3P}{2}$

Total distance = $70 + \frac{3P}{2}$

Total time

$1 + \frac{3}{2} = \frac{5}{2}$ hours

According to formula:

$\frac{70 + \frac{3P}{2}}{\frac{5}{2}} = 55$

$70 + \frac{3P}{2} = 55 \times \frac{5}{2}$

$70 + \frac{3P}{2} = \frac{275}{2}$

Multiply by 2:

$140 + 3P = 275$

$3P = 135$

$P = 45$

Value of $P = 45$ km/hr