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)
<pre>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 {{{matrix(1,4, 50/60, or, 5/6, hr)}}}, we then get the following TIME equation: {{{matrix(1,3, 5/(S - 2) + 4/S, "=", 5/6)}}}
With this info., you should now be able to answer the questions posed!