Suppose you have entered an 81-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 7 miles per hour, and during your bicycle race, your average velocity is 30 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?

Mathematics · High School · Mon Jan 18 2021

llm

Answered on Wed Oct 19 2022

Let the number of hours travelled by 7 mph be x

And, number of hours travelled by 30 mph is y

Then, according to question

x + y = 5 …1

7x + 30y = 81 …2

Using elimination method :

Multiplying equation 1 by 7, we get

7x + 7y = 35

Subtracting equation 2 from 1, we get

7x + 30y - 7x - 7y = 81 - 35

23y = 46

y = 46/23

y = 2

Now, putting value of y in equation 1, we get

x + 2 = 5

x = 5 - 2

x = 3

Now, distance travelled by running = 7 × 3

= 21 miles

Distance travelled by bicycle = 30 × 2

= 60 miles