Expert: Jenny - 10/14/2004

Question
Carlos and Maria drove a total of 258 miles in 5 hours.  Carlos drove the first part of the trip and averaged 53 miles per hour.  Maria drove the rmainder of the trip and averaged 51 miles per hour.  For approximately how many hours did Maria drive?  Round your answer to the nearest tenth if necessary.


Having trouble coming up with setting up the equation.  I know d=rt, but I can not get the two seperate people driving different rates.


Answer
Hi Diane,

Let's see if we can figure this out. You're right on with the d=rt, so in our case, 258=5*r.  We know that Carlos and Maria split the driving time, but we don't know how long either of them drove. So, we'll let Carlos' driving time equal x, and Maria's driving time equal 5-x, because x+5-x=5 hours, the total trip.

So, we now have 258=(Carlos' portion)+(Maria's portion)
Carlos' rate is 53mph and Maria's is 51mph.  So, we have:

258=(x)(53)+(5-x)(51)

If we simplify this, we can solve for x and find out how long each drove!

So,

258=53x+255-51x
258=2x+255
3=2x
3/2=x

So, Carlos drove 1 1/2 hours of the trip, meaning Maria drove 3 1/2 hours. (Poor girl :( ... ) We can double check this by making sure that 1 1/2 (53) + 3 1/2 (51) = 258

79.5+178.5=258

There you go! I hope this helps!