1. ## word problems

a man drives 108 km at an average rate. If he had driven 5km/hr. faster, he would have made the trip in 15 hours less time. How fast did he drive?

2. ## Word Problem

You know that $Time = \frac {Distance}{Speed}$.

Distance $= 108$ km

Speed $= s$ km/h

If he had driven $5$ km/hr faster, he would have reached in $15$ hours less time.

That means... Actual Time taken $-$ Time taken while driving $5$ km/h faster $= 15$ hours.

$\Rightarrow \frac {108}{s} - \frac {108}{s + 5} = 15$

Now express as a single fraction:

$\Rightarrow \frac {108 (s + 5) - 108s}{s (s + 5)} = 15$

Now multiply both sides by the denominator, $s (s + 5)$.

$\Rightarrow 108 (s + 5) - 108s = 15s (s + 5)$

$\Rightarrow 108s + 540 - 108s = 15s^2 + 75s$

$\Rightarrow 540 = 15s^2 + 75s$

$\Rightarrow 15s^2 + 75s - 540 = 0$

Divide throughout by $15$:

$\Rightarrow s^2 + 5s - 36 = 0$

Now factorise:

$\Rightarrow (s + 9) (s - 4) = 0$

$\Rightarrow$ Either $s = -9$(discard) or $s = 4$.

Check: So he was driving at $4$ km/h.

Time taken to drive at $4$ km/h $= \frac {108}{4} = 27$ hours.

Time taken to drive at $9$ km/h $= \frac {108}{9} = 12$ hours.

Difference in times $= 27 - 12 = 15$ hours.

at above poster.

I hope that helps.

ILoveMaths07.