How long from when they start do they meet?

Ruth and Crony cycle toward each other, beginning 138 km away at the same time. Ruth cycles at 13 km/h and Crony cycles at 12 km/h. 1 hour after they start, Crony stops and repairs her bicycle for 1 hour. Then she keeps cycling. How long from when they start do they meet?

1 Answer

6 hours


Let's work this out piece by piece.

First we have the two people 138 km apart. They travel towards each other for 1 hour at a collective speed of 25 km/hr (Ruth at 13 and Crony at 12). So after 1 hour, they are:

#138-25=113# km apart

Crony needs to stop and repair her bike for an hour, and so for that hour Ruth continues to ride toward Crony:

#113-13=100# km apart.

With Crony's bike fixed, they now ride towards each other again. By observation, we can see it'll take 4 hours:

#(100 km)/(25(km)/(hr))=4hr#

In total, it takes them 6 hours to meet.