Rational Equations

Question

1.During the winter Olympics, a downhill skier had to complete two qualifying heats to make it to the metal round. She finished her first run in 2 minutes and her second run in 3 minutes. Both runs took place on a course that was 4.3 km long. What was her average speed? Write answer as a whole number or as a decimal rounded to the nearest 10th. Show all work.  

2.Two groups of friends are taking taxis to a party in Greenville. The first taxi leaves from the financial district and travels at 45 km/h. At the same time, the other taxi leaves from the marina and travels 62 km/h. The two taxis are 14 km apart and heading directly towards each other. How much time will it take for the taxis to meet? If necessary, round your answer to the nearest minute. Show All Work. 

Answer 1

It is important to remember that:

Average Speed = Total Distance

                                  Total Time

                            = (4.3 km + 4.3 km)/(2 min + 3 min)

                            = 8.6 km/5 min

                            = 1.7 km/min

#2

Let D1 = Distance of 1^st taxi

      D2 =Distance of 2^nd taxi

D1 + D2 = 14 km

    (45 km/hr)t + (62 km/hr)t = 14 km                   Both taxis travel for the same time: t.

             t (107 km/hr) = 14 km

             t = (14/107 hr) x 60 min/hr

             t = 8 min

Answer 2

Jacob,

For the first problem, you are looking for the average speed over two runs. First, you need to find the speed of each run.

The first run she went 4.3 km in two minutes. So, her speed was 4.3km/2min = 2.15 km/min

The second run she went the same distance in three minutes. So, her speed was 4.3 km/3 min = 1.43 km/min

Now we need to find her average speed. To find the average, you add the numbers together and divide however many numbers there are total, in this case 2.

So, average speed is (2.15 + 1.43) / 2 = 1.79 km/min

Hope this helps