algebra 1 word problem. rate

Question

at 9:00 on sunday morning, two bicyclists heading in opposite directions pass each other on a bicycle path. the bicyclist heading north is riding 7 km/hr faster than the bicyclist heading south. at 10:30, they are 43.5 km apart. find the two bicyclists' rates.

Answer 1

Hello, looks to me like we need to use the distance formula d=r(t)

the distance is given, we find the difference between the times to get the time traveled, and we need to add the speed, or rate, to get a total combined speed.

***if 1 person is going 2mi/hr and another is going in the opposite direction at the same rate, then they are moving apart at a rate of 4mi/hr.

we apply this idea and say the first bike is unknown (x) and the 2nd is going 7km/hr faster than the first. Values are shown below. Then we just start simplifying.

43.5(km) = [x+(x+7)]1.5

43.5 = (2x + 7)1.5

43.5 = 3x + 10.5

33 = 3x

x = 11

so the first bike is going 11km/hr and the 2nd would be 18km/hr. But don’t forget to check your work. Combine the two speeds, plug it back in the formula and make sure you get the right distance of 43.5km

43.5 = 29(1.5)

43.5 = 43.5

looks like a true statement to me :-) great question!