# Math

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)

1. 👍
2. 👎
3. 👁
1. 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

1. 👍
2. 👎

## Similar Questions

1. ### Math

in a triathlon , an athlete swims 750m in 15 minutes, cycles at an average speed of 40km/h for 30 minutes and runs 5 km at an average speed of 3m/s . find his average speed for the entire competition giving your answer in km/h

2. ### math

For his exercise today, Josh plans to both run and swim. Let r be the number of laps he runs and let s be the number of laps he swims. Each lap he runs takes him 4 minutes, and each lap he swims takes him 3 minutes. He wants to

3. ### math

during a triathlon, Sharon swims 1/4 of the total route and cycles 3/5 of the remaining route. she runs the rest of the route. if she runs 3,600 meters, find the total distance of the triathlon route. show your work.

4. ### algebra

A contestant on a game show must guess the price of a new car. The contestant will win if his guess is within \$1000 of the price of the car. If the price of the car is \$24,995 and the contestant's guess is represented by g, what

1. ### Maths

A student cycles for xhours at 12km/hr and y hours at 16km/hr.Altogether,the student cycles 66km/hr in 5hrs.find the values of x and y

2. ### physics

A game show contestant won a prize by pushing a bowling ball 20 m using her nose. The amount of work done was 1470 J. How much force did the contestant exert on the ball?

3. ### Math

Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 7/8 of the route, and swims the rest of the way. She swims 0.9 miles. Find the total distance of the triathlon route.

4. ### Math

8. Sylvia is training for a triathlon. she cycles 6.25 km in 25 min. a) What is her average speed, in kilometres per hour? b) Solve a proportion to determine how long she would take to cycle 40 km. Us the speed in part A)

1. ### pre algebra

Lilliana is training for a marathon. She runs the same distance every day for a week. On Monday, Wednesday, and Friday, she runs 3 laps on a running trail and then runs 6 more miles. On Tuesday and Sunday, she runs 5 laps on the

2. ### Maths Algebra Application Practice

In a TV trivia show, a contestant receives 500 points for a correct answer and loses 200 points for an incorrect answer. Let c represent the number of correct answers and i represent the number of incorrect answers. What is the

3. ### physics

A river has a steady speed of 0.640 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point. (a) If the student can swim at a speed of 1.15 m/s in still water, how long does the trip take? (b) How

4. ### Maths

In a triathlon, Farhan swims a distance of 1.5 km at an average speed of 2.5 km/h, cycles 40 km in 1/1/2 hours and runs at an average speed of 9 km/h for 1/1/9 hours