Question

A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed. [4 MARKS]

Answer 1

Framing the equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Let the usual speed of the plane be $x$ km/hr. Then,

Time taken to cover 1500 km with the usual speed $=\frac{1500}{x}hrs$

Time taken to cover 1500 m with the speed of $(x+250)km/hr=\frac{1500}{x+250}$

$\therefore \frac{1500}{x}=\frac{1500}{x+250}+\frac{1}{2}$

$\Rightarrow \frac{1500}{x}-\frac{1500}{x+250}=\frac{1}{2}$

$\Rightarrow \frac{1500x+1500\times 250-1500x}{x(x+250)}=\frac{1}{2}$

$\Rightarrow \frac{1500\times 250}{x^2+250x}=\frac{1}{2}$

$\Rightarrow 750000=x^2+250x$

$\Rightarrow x^2+250x-750000=0$

$\Rightarrow x^2+1000x-750x-750000=0$

$\Rightarrow x(x+1000)(x-750)=0$

$\Rightarrow x=-1000or,x=750\Rightarrow x=750$ [$\because$ speed cannot be negative]

Hence, the usual speed of the plane is 750 km/hr.