Question

A student starts for a hostel 24 km away from his house on cycle. If he increases his
speed by 2 km per hour, he reaches 2 hour early. Find out his speed km per hour.
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Answer 1

If I let distance $D$, time $T$, speed $S$, three variables satisfies the expression

$D=T\times S$

'A student starts for a hostel 24 km away from his house on cycle.'

Distance is 24 km.

Let time he spent $T_1$ hour.

And let speed $S_1$ km/h.

∴ $24=T_1\times S_1$ --- 1

'If he increases his  speed by 2 km per hour, he reaches 2 hour early.'

Distance is 24 km.

Time he spent is $T_1-2$ hr.

And speed is $S_1+2$ km / h.

$24=(T_1-2)\times (S_1+2)$ --- 2

Expand the expression above.

$T_1\times S_1+2T_1-2S_1-4=24$

We know that $T_1\times S_1=24$.

$24+2(T_1-S_1)-4=24$

$T_1-S_1=2$

∴ $S_1=T_1-2$ --- 3

Substitute 3 into 1

$T_1\times(T_1-2)=24$

$T_1^2 -2T_1-24=0$

$(T_1-6)(T_1+4)=0$

As $T_1>0$, $T_1$ is 6.

∴ $T_1=6$ hr

∴ $S_1=4$ km / h

His speed is 4 km / h.

T h a n k

y o u .