A man drives from Mzumbe to Kibaha,a distance of 48km in 45min. Where the surface is good he drives at 72km/h, where the surface is bad he drives at 48km/h. Find the number of kms of good surface.

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- Dec 8th 2008, 01:16 AMMTAALAMUHelp with problem
A man drives from Mzumbe to Kibaha,a distance of 48km in 45min. Where the surface is good he drives at 72km/h, where the surface is bad he drives at 48km/h. Find the number of kms of good surface.

- Dec 8th 2008, 03:33 AMearboth
Let x denote the number of kilometers of the road in good condition. Then (48 - x) is the number of kilometers of the road in bad condition.

From the definition of $\displaystyle speed = \dfrac{distance}{time}$ you get $\displaystyle time = \dfrac{distance}{speed}$

Now you can set up an equation in x:

$\displaystyle \dfrac x{72} + \dfrac{48-x}{48}=\dfrac{45}{60}$

(Keep in mind that the speed is given in kilometers per**hour**and the elapsed time in minutes, which have to be changed to hours too!)

Solve the equation above for x. I've got x = 36 km. Consequently the bad road is 12 km long.