At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 6 km/hour faster than the bicyclist heading south. At 10:15, they are 42.5 km apart. What are their rates?
We need to set up equations based on the known information. I always write down everything the question gives me and try to link the information with logic or established formulas. I automatically think of speed=distance/time in this case. Also, units are important, so decide what you want to use and stick with them for all calculations. I will use km and hours.
Okies, the total distance travelled by both cyclists is 42.5 km. This means that the sum of the distances will be 42.5 km. Let's use
Rearrange the speed formula to give the distance travelled as speed multiplied by time. We will use
Remember that the northward bound cyclist is going 6 km/hour faster, so:
At this point, we want to solve equation (1), so we need to replace either
Now substitute (4) into (1) to solve for
Now we know the distances travelled by both so we use speed = distance/time to get the rates: