Karen took 5 hrs to drive 470 km. For part of the trip she drove at 100 km/hr for the rest she drove 90 km/hr. How far did she drive at each speed?

Question

This word problem is on a practice for a test tomorrow and I just can't get it.  Have worked on it for over an hour and am beyond frustrated.  Know the answers are 200 km at 100 km/hr and 270 km at 90 km/hr but do not know how to write it out in long form algebra, please help

Answer 1

Brian,

 

Don't get frustrated. 

 

You will first need to understand rates via the following equation:

 

Rate = distance/time 

 

From the given information, we know that Karen traveled 470mi in 5 hours. By manipulating the rate formula from above we see that:

 

rate * time = distance 

 

We are given information that will allow us to use the product-sum rule to the left side of the "newly" manipulated rate equation.

 

We know that she traveled 100km for a portion of the time and 90km for the remaining portion. Let t represent this piece of information.

 

The working information is "plugged" into the following equation:

 

100t + 90(5-t) = 470

100t + 450 - 90t = 470

10t = 20

 

t = 2 this will be how long she traveled at 100km.