Christy went on a round-trip bicycle ride starting at her house. when she left, she traveled downhill at a rate of 24 kilometers per hour (kph). she rested for 30 minutes, and then returned to her house. since the return trip was partly uphill, it took half an hour longer and christy averaged only 20 kph. how long did the return trip take?

Since this is a round-trip, Christy covered the same distance in both journey.

Let the distance covered be


When she left the house, she travelled at


We were given the average speed to be


Meaning if we add the speed in the return journey to 24 kph and find the average , we must obtain 20 kph.

Let

be the speed in the return trip.

Then


We solve for x to obtain;





We were also told that she took half an hour longer in the return trip.

If we let

represent the time the first journey took, then the return trip will take



Now we have the following:















Now let us equate the two equations to obtain,



We expand and simplify to obtain;



This implies that,



.




Hence the return trip took,



hours.