# A boy was going home for 12km. We went 2km/h faster than last time and now spent 1 hour less on the road. How fast was the boy going?

##### 2 Answers

#### Explanation:

If the boy travelled at

#12/x - 12/(x+2) = 1#

Multiplying through by

#12(x+2)-12x = x(x+2)#

That is:

#24 = x^2+2x#

Adding

#25 = x^2+2x+1 = (x+1)^2#

Hence

So

That is:

Since the time must be non-negative, the applicable solution is

The later traveling speed was 6 km/h

#### Explanation:

Let initial velocity be

Let new velocity be

Let initial time be

Let new time be

Known that velocity x time = distances

Given that

Given that

Using equation(1) substitute for

Set

Multiply by

Multiply by -1

We need