Karim occasionally cycles the 24km journey to school. When he hurries and increases his normal average speed, v, by 6km/h his journey time is cut by 40 minutes. How long does it normally take him to cycle to school?

2. rt=24

He increases his speed by 6, (r+6)

He decreases his time by 2/3 hours, t-2/3

(r+6)(t-2/3)=24

But r=24/t

((24/t)+6)(t-2/3)=24

Solve for t.

3. How do I expand it?

(6 + (24/t))(t - (2/3)) = 24

I tried using foil and got the stage:

6t + 20 .... = 24

The .... represents -(2/3) * (24/t).

How do I do that?

4. Originally Posted by Jehan
How do I expand it?

(6 + (24/t))(t - (2/3)) = 24

I tried using foil and got the stage:

6t + 20 .... = 24

The .... represents -(2/3) * (24/t).

How do I do that?
Perhaps coding it will make things a bit clearer:
$\displaystyle \left ( 6 + \frac{24}{t} \right ) \left ( t - \frac{2}{3} \right )$

$\displaystyle 6 \cdot t + 6 \dot -\frac{2}{3} + \frac{24}{t} \cdot t + \frac{24}{t} \cdot - \frac{2}{3}$

Can you see how to do this step now, and can you continue?

-Dan