290,523 views
27 votes
27 votes
Two cyclists, 45 miles apart, start riding towards each other at the same time……..

Two cyclists, 45 miles apart, start riding towards each other at the same time……..-example-1
User Sidhuko
by
2.3k points

1 Answer

26 votes
26 votes

Given:

Two cyclists, 45 miles apart, start riding towards each other at the same time.

Required:

We need to write the equation using the given information and to calculate the speeds of two cyclists.

Step-by-step explanation:

(a)

Let us consider r is the speed of slower cyclist.

Distance covered by slower cyclist,


r*3

Distance covered by faster cyclist,


2* r*3

Total distance is 45 miles.

Now from this data, we can say that


\begin{gathered} 2* r*3+r*3=45 \\ 6r+3r=45 \\ 9r=45 \end{gathered}

(b)

From part (a)


9r=45

By simplifying, we get


\begin{gathered} r=(45)/(9) \\ r=5 \end{gathered}

This is the Speed of the slower cyclist.

Hence speed of the faster cyclist is 2 times as fast as the slower cyclist.

Therefore, speed of the faster cyclist is


\begin{gathered} =2*5 \\ =10 \end{gathered}

Final Answer:

(a)


6r+3r=45

(b)

The speeds of both the cyclists is 5 miles per hour and 10 miles per hour.

User Debe
by
2.7k points