SOLUTION: Amber has entered a cross-country running series. Each race in the series has a time limit by which runners must complete the course in order to qualify for the next race. The

Question 1177891: Amber has entered a cross-country running series. Each race in the series has a time limit by which runners must complete the course in order to qualify for the next race.

The first race is 9 km long and must be completed in 50 minutes.
After Amber runs the first 5 km, her coach informs her she must increase her speed by 2 km/h for the last 4 km in order to finish the race in 50 minutes.
a.Complete the following chart. (3 marks)

First 5 km Section
Distance (km)
Speed (km/h)
Time (h)

Last 4 km Section
Distance (km)
Speed (km/h)
Time (h)

b.Write and solve a rational equation to determine the speed at which Amber needs to run the last 4 km of the race. Convert time in minutes to time in hours. (2 marks)

Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
4/x + 5/(x+2) = 5/6
(4x+8 +5x)/x(x+2) = 5/6
6(9x+8)= 5x(x+2)
54x+48 = 5x^2 +10x
5x^2 +10x -54x -48=0
5x^2-44x -48 =0
First 5 km Section
Distance (km) 5
Speed (km/h) x
Time (h) 5/x
Last 4 km Section
Distance (km) 4
Speed (km/h)x+2
Time (h) 4/(x+2)
5/x + 4/(x+2) = 5/6
(5x+10 +4x)/x(x+2) = 5/6
6(9x+10)= 5x(x+2)
54x+60 = 5x^2 +10x
5x^2 +10x -54x -60=0
5x^2-44x -60 =0
x=10
Last 4 km at 12 km/h

Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

Amber has entered a cross-country running series. Each race in the series has a time limit by which runners must complete the course in order to qualify for the next race.

The first race is 9 km long and must be completed in 50 minutes.
After Amber runs the first 5 km, her coach informs her she must increase her speed by 2 km/h for the last 4 km in order to finish the race in 50 minutes.
a.Complete the following chart. (3 marks)

First 5 km Section
Distance (km)
Speed (km/h)
Time (h)

Last 4 km Section
Distance (km)
Speed (km/h)
Time (h)

b.Write and solve a rational equation to determine the speed at which Amber needs to run the last 4 km of the race. Convert time in minutes to time in hours. (2 marks)

Let speed needed to run last 4 km, be S
Then speed needed to run the first 5 km = S - 2
With 50 mins being , we then get the following TIME equation:
With this info., you should now be able to answer the questions posed!
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