In a triathlon, a contestant swims 5 km, cycles 30 km, and then runs 20 km. In general, a contestant runs at an average speed of x, swimsat an average speed of x/5, and cycles at an average speed of 5x, where x is in kilometres per hour.
a) Determine an expression for the total time taken to complete the race. (2 marks)
b) Cynthia can swim at 2 km/h. How long will it take her to complete the race? (1 mark)
c) If Shaitha can cycle at 40 km/h, how much longer will it take her to complete the race, compared to Cynthia? (1 mark)
time = distance/speed
5/(x/5) + 30/(5x) + 20/x
= 25/x + 6/x + 20/x
= 51/x
she has gone 5 + 30 + 20 = 55 km
b)
2 = x/5
so x = 10
and time = 51/10 = 5.1 hr
c)
40 = 5x
x = 8
time = 51/8 = 6.375
difference = 6.375 - 5.1 = 1.275
a) To determine the total time taken to complete the race, we need to calculate the time taken for each leg of the triathlon and then sum them up.
The time taken for the swimming leg can be calculated using the formula: time = distance / speed.
So, the time taken for swimming is: 5 km / (x/5) = 25 / x hours.
The time taken for the cycling leg can be calculated using the formula: time = distance / speed.
So, the time taken for cycling is: 30 km / (5x) = 6 / x hours.
The time taken for the running leg can be calculated using the formula: time = distance / speed.
So, the time taken for running is: 20 km / x = 20 / x hours.
Therefore, the total time taken to complete the race is the sum of these three times:
Total time = time for swimming + time for cycling + time for running
= 25 / x + 6 / x + 20 / x
= (25 + 6 + 20) / x
= 51 / x hours.
b) If Cynthia can swim at 2 km/h, we can substitute x = 2 in the above expression to find her total time:
Total time = 51 / 2 = 25.5 hours.
c) If Shaitha can cycle at 40 km/h, we can substitute x = 40 in the above expression to find her total time:
Total time = 51 / 40 = 1.275 hours.
To compare with Cynthia's time, we subtract Cynthia's time from Shaitha's time:
Difference in time = Shaitha's time - Cynthia's time
= 1.275 - 25.5
= -24.225 hours.
Therefore, Shaitha will take approximately 24.225 hours longer to complete the race compared to Cynthia.
a) To determine the total time taken to complete the race, we need to sum up the time taken for each segment of the triathlon.
The time taken to swim 5 km can be calculated by dividing the distance by the average swimming speed, which is x/5 km/h. So, the time taken to swim is 5 / (x/5) = 25/x hours.
The time taken to cycle 30 km can be calculated by dividing the distance by the average cycling speed, which is 5x km/h. So, the time taken to cycle is 30 / (5x) = 6/x hours.
The time taken to run 20 km can be calculated by dividing the distance by the average running speed, which is x km/h. So, the time taken to run is 20 / x = 20/x hours.
To find the total time, we add up the time taken for each segment:
Total time = time taken to swim + time taken to cycle + time taken to run
= 25/x + 6/x + 20/x
= (25 + 6 + 20) / x
= 51 / x hours.
Therefore, the expression for the total time taken to complete the race is 51 / x hours.
b) Let's substitute Cynthia's swimming speed, which is 2 km/h, into the expression for the total time:
Total time = 51 / x hours.
Substituting x = 2, we get:
Total time = 51 / 2 = 25.5 hours.
Therefore, it will take Cynthia 25.5 hours to complete the race.
c) To determine the time it will take Shaitha to complete the race, we need to substitute her cycling speed, which is 40 km/h, into the expression for the total time:
Total time = 51 / x hours.
Substituting x = 40, we get:
Total time = 51 / 40 = 1.275 hours.
To compare Shaitha's time with Cynthia's time, we subtract Cynthia's time from Shaitha's time:
Difference in time = Shaitha's time - Cynthia's time
= 1.275 - 25.5
= -24.225 hours.
Therefore, Shaitha will take 24.225 hours longer to complete the race compared to Cynthia.