Question
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)
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)
Answers
Damon
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
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